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Paranoidhuman ( talk) 10:29, 14 May 2010 (UTC)
I have seen mentions in the literature of the Schrödinger group in an increasing number of contexts (aging situations, potentials in AdS). I think the article would benefit from some discussion of the group, but I do not know enough about to author a section. —Preceding unsigned comment added by 128.173.125.74 ( talk) 15:33, 13 October 2009 (UTC)
shouldnt the formula where kinetic energy + potential have hbar squared instead of hbar? —Preceding unsigned comment added by 62.136.133.147 ( talk) 13:57, 17 May 2008 (UTC)
Dan Gluck added a subsection to this article making a few spelling mistakes, which Pfalstad corrected. However, there are also a few minor flaws in the content, e.g., particle mass μ of the electron. No electron was mentioned earlier and mass is indicated by M. Before I (or somebody else) correct(s) these minor things, I like to know whether we all agree that this article is the place for Dan's addition. In the list of analytic solutions we find two articles that treat the spherical symmetric problem. If Dan is not satisfied with these two articles, maybe he should improve those. To me Dan's addition seems fairly arbitrary, he could have added to the present article any solution from the list of analytic solutions. Any comments?-- P.wormer 15:24, 22 May 2007 (UTC)
As a professor in physics from Denmark, I am very disappointed, I am concerned because the English written articles have a tendency to penetrate into all other languages. This article has so many errors/misunderstanding that a GA-status will harm the Wikipedia. Quantum mechanics do not need to be presented as something very complicated, and the use of the Dirac's notation is throughout the article completely wrong. Sincerely j.h.povlsen 80.163.26.74 00:36, 13 August 2007 (UTC)
And I emphasize again, that this article does not present the work of Schroedinger, The same article could as well have been about the equations of Heisenberg. The article starts in it's very first equation with a misinterpretation of the Dirac notation, and then it goes on by describing a Complex Hilbert Space. Let me you remind, that Schroedinger was not aware of any of the above mentioned complexities about the world. He was a physicist, and his equation did not just jump out from nothing! He thought, without a thought on Hilbert space, but on the "quantum mechanics" as he knew it at that time. And the quantum mechanics was the discoveries from Planck, Bohr, Luis de Broglie and Einstein. The Planck/Einstein discovery was, that the energy quantization of light/(Electro-magnetic waves) could be expressed as
while Luis de Broglie discovered a relation between momentum and wavelength
In connection with that the energy, according to Newton, consists of a kinetic part and potential part as in
he looked at a monochromatic wave , and realized that the energy could be evaluated as an eigenvalue to
and a momentum component , similarly could be derived as an eigenvalue to
And by inserting this into the Newton energy rule he reached his named equation:
which (in Wikipedia) sadly, seems to become an untold story. I hope some one, some day will tell it. Sincirely j.h.povlsen 80.163.26.74 04:40, 15 August 2007 (UTC)
We can find stationary solutions to the Schrodinger by looking at solutions separable in time and space as: which inserted into the time dependent Schoedinger equation reveal solutions on the form with the time independent part being an eigenfunction to:
where is interpreted as the energy. This equation can be analytically solved for a number of very physical important cases such as the Coulomb potential (orbitals in the hydrogen atom), and the harmonic oscillator (lowest order approximation of arbitrary potential functions around a minimum). "
The quantum mechanics need in a proper formulation to include the classical mechanics in it's macroscopic limit, and the Shroedinger equation does indeed that, as realized by Ehrenfest. Ehrenfest showed from the time dependent Schroedinger equation that the the expectation value , defined as
of a pysical operator (i.e. a Hermetian operator) evolves in time as
where , the Hamiltonian is and denotes the commutator defined as
and by considering the posiotion operator and the momentum operator he derived the correspondance equations
In agreement with Newtons second law.
Sincirely 80.163.26.74 00:01, 17 August 2007 (UTC)j.h.povlsen
From artical
and similarly since: 1: then 2: and hence 3:
I agree with formula 1 and 2 as currently derived however I derive a different answer for formula 3:
So how does this get accounted for? (the problem points are denoted )-- ANONYMOUS COWARD0xC0DE 23:51, 4 September 2007 (UTC)
Someone should go back through this article and change the sloppy notation for the wavefunction Psi. Psi is a function of x and t, while psi is one a function of x. This can wildly confuse a physicist or student looking for mathemetical expressions described by the Schrodinger Equation. Perhaps putting the wavefunction in the form of its variables Psi(x,t) and psi(x) can alleviate this confusion. —Preceding unsigned comment added by GaiaMind ( talk • contribs) 05:29, 28 October 2007 (UTC)
Referring to the state vector as "one dimensional" is misleading; it is typically infinite dimensional Peter1c 07:29, 7 November 2007 (UTC)
In order to uphold the quality of Wikipedia:Good articles, all articles listed as Good articles are being reviewed against the GA criteria as part of the GA project quality task force. While all the hard work that has gone into this article is appreciated, unfortunately, as of February 15, 2008, this article fails to satisfy the criteria, as detailed below. For that reason, the article has been delisted from WP:GA. However, if improvements are made bringing the article up to standards, the article may be nominated at WP:GAN. If you feel this decision has been made in error, you may seek remediation at WP:GAR. I've had to delist this article from GA status as part of the good article quality control sweeps. It lacks inline references which became a good article requirement in 2006, possibly after this article was passed. I've listed this article at our unreferenced good article task force. Once adequate inline sources have been added, hopefully the article can easily reattain GA status. -- jwanders Talk 12:26, 15 February 2008 (UTC)
I am in the process of cleaning up the article via my sandbox version. Feel free to comment on it. Thanks. MP ( talk• contribs) 12:14, 17 February 2008 (UTC)
Upon request, I've just rewritten the article with my sandbox version. A lot more work still needs to be done though. MP ( talk• contribs) 17:09, 8 March 2008 (UTC)
I decided to remove the subsections Schrodinger wave equation and wave function as I think there is no point in repeating what's already been said in the article and a lot of the stuff will not help to actually understand the Schrodinger equation per se. Hope this is ok; comments/criticisms welcome. Thanks. MP ( talk• contribs) 06:53, 14 March 2008 (UTC)
I've always seen the time-dependent wavefunction written with a capital psi and the time-independent function with a lowercase one, e.g. . It took me a moment to work out what the article was talking about as a result. Is there a particular notation used by most physicists, or was my physics textbook just using an unconventional convention (so to speak)? — Xaonon ( Talk) 19:37, 27 March 2008 (UTC)
Is it really necessary to add 'citation needed' 3-4 times per sentence? It's unreadable. Put a sentence in the beginning to give a conceptual (useless) description, then give the math for people who want to know. To paraphrase Lord Kelvin, if you cannot quantify it, you don't know what you're talking about. —Preceding unsigned comment added by 70.249.215.163 ( talk) 22:58, 27 March 2008 (UTC)
this article is too complex to be comprehended by general public. this article presume the reader to have an advanced understading and knowledge in the subject. a less mathematical approach, a more conceptual approach is required for people who have limited knowledge in physics and mathematics. I suggests to remove the more complex parts from this page into a new article. So that it would be possible for general reader to understand this subject. —The preceding unsigned comment was added by 202.152.240.246 ( talk) 15:22, 2 May 2007 (UTC).
I dissagree with the wording that an electron is a microscopic paricle, its smaller than that! Noosentaal ( talk) 17:53, 7 April 2008 (UTC)
I think that one should not present pseudo-history as history. It is possible to give modern mathematical derivations, but in a historical discussion I think it is good to stick to the actual events, if not the exact formulas. Likebox ( talk) 02:44, 15 May 2008 (UTC)
Too much detail is just as bad as too little. The person who is reading this page should be able to reproduce elementary algebraic manipulations. Likebox ( talk) 21:58, 15 May 2008 (UTC)
(deindent) Maybe you're right, I am not so great with psychology. But I think that the previous argument was essentially identical, except it was done with more detail to make the algebraic steps more explicit. The issue I had with that (and I might be psychologically totally off base here) is that I think it makes the reader lose the forest for the trees. It had many equations whose only purpose was to restate the equivalence of E and \omega and p and k. By doing this, a larger fraction of the "steps" are easier to follow, but only because the number of steps is made larger by including more algebraic restatements of p=hk. So, it would say "p=hk" and later "k=i d/dx \psi" and later "p=i\hbar d/dx". This sort of thing bothered me when I was a student (At least I think I remember that it did) because it would obscure the essentially new insights--- in this case the substitution of derivative operators in the energy equation--- by hiding them among a list of algebraic manipulations which should be internalized by the reader first, before doing anything else. But perhaps its the exact opposite. Maybe if there are more familiar identities, there is a feeling of familiarity which aids the process of understanding.
The group-velocity stuff might be an unnecessary hurdle for a first read, and it might need to be removed. You might also be right that a careful restatement of p=hk multiple times will reinforce understanding, because different people might "click" on different restatements. I have no confidence that the current version is any good at all. The previous presentation might be significantly better. Probably this is best figured out by asking some students who have just finished learning quantum mechanics.
About Schrodinger and Copenhagen--- I read conflicting stuff on this. Everybody agrees that at first, he hated the Copenhagen interpretation, and thought \psi was a physical charge density or something, but after Born's paper he (and Einstein and everyone else) came to agree that, given the formalism, a statistical interpretation is the only sensible one. The question that remains is whether he held out hope that this was a statistical approximation to an underlying determinisic DeBroglie-Bohm theory, or if he had some Wigneresque proto-Everettist ideas. This I don't know for sure. In the new Einstein biography by Isaacson, the author states that Schrodinger was sympathetic to Einstein's view at least up to EPR, but in the 1940s goes on a rant to someone or other about how Einstein was a stupid old man when it came to quantum mechanics. That's why I assumed he had come to accept that the Copenhagen interpretation is correct. If you have better information, please fix it. I don't have any insight into Schrodinger's thinking. Likebox ( talk) 20:14, 18 May 2008 (UTC)
"Schrödinger tried unsuccessfully to interpret it as a charge density." This is a very interesting claim! In the history of relativistic QM, it is well known that the Klein-Gordon equation was originally discarded because its wavefunction failed to fit the probability interpretation. BUT! In modern QFT, the Klein-Gordon equation is actually correct -- the wavefunction just has to be interpreted as charge density rather than probability. So if Schroedinger really started out interpreting the wavefunction as charge density, and considering that he also preceded Klein and Gordon by trying that equation before trying the one he is now known for, surely there is more interesting history worth telling here (or at least, the Klein-Gordon page needs a better history section). Cesiumfrog ( talk) 05:01, 31 May 2008 (UTC)
There is a difference between believing that the Copenhagen interpretation is incorrect or incomplete and believing that the statistical interpretation of the wavefunction is incorrect. While I don't know for sure whether Schrodinger believed that the Copenhagen interpretation was a final statement on the nature of physical reality, I am sure that, like Einstein and everybody else, he accepted Born's analysis as correct and realized that the wavefunction could only be interpreted as a probability. This was a universal conclusion, everyone agreed with Born's interpretation. For example, Einstein is directly quoted in Isaacson as saying that the only possible interpretation of the wavefunction is statistical, that this is an unavoidable conclusion. This was (and still is) such a clear fact that I can't imagine Schrodinger rejected it. He certainly understood, although I'm sure with distaste, that the probability is proportional to the wavefunction squared (although perhaps with a philosophy radically different than those that were codified by Bohr). His often quoted dislike of quantum discontinuities should be properly read as a sign that he initially wanted to avoid all quantum jumps with a continuous wave formalism, but failed. I don't have any insight into whether he thought that quantum mechanics was a statistical approximation to a deeper underlying theory. Likebox ( talk) 00:17, 20 May 2008 (UTC)
This article has undergone a major sequence of changes, the second last (before my revert) of which (by an anon.) completely obliterated crucial info. on the forms of the Schrodinger equation, but kept a mass of mathematical detail that is not relevant to the article or point being made at hand. I intend to sort out this article at some point. There is too much maths which could - and should - be moved to articles dealing with those issues more directly. MP ( talk• contribs) 18:44, 13 June 2008 (UTC)
The section "nondegenerate ground state" contains an incorrect proof that the ground state of a Schrodinger equation is a nonnegative function and nondegenerate. A while ago the proof was replaced by a better one but then reverted back.
I located this wikipedia article while looking for a proof of this well known property. While it is not clear whether the proof belongs here in this article, let me first say why the proof as it stands is wrong.
The proof is based on the variational principle. The proof shown currently is that if is a test function that changes sign and minimizes the energy functional then we can take as another test function that has the same integrals of potential and kinetic energy, except for the kink at the place where . The kink should then be smoothed out, and the result is that we now have a test function that has a smaller value of the energy functional. This contradiction proves the statement.
This is incorrect because it's not true that we can always straighten the kink while not increasing the energy functional. An easy counterexample is and . The kinetic energy of this is identically zero, so . If we now take and straighten the kink, the kinetic energy is going to be strictly positive no matter how smoothly we straighten it. So the new test function has always a strictly greater value of the energy functional. This counterexample shows that it is not possible to smooth the kink as required.
The proof that was deleted by an edit on 31 August was better: it allowed a small increase of the energy functional while straightening the kink.
I'd like some experts in mathematical physics to examine this argument. In my view the proof of this important statement needs to be either presented clearly and correctly, or removed and replaced by a reference to a textbook. Sznagy ( talk) 14:35, 9 & 13:52, 11 September 2008
The problem with all the hbars is that for a new person, each symbol is intimidating. The fewer symbols the better. In this case, the constant is only performing a unit conversion, and so should not be included except:
When talking about abstract theorems, like the positivity of the ground state wavefunction, the hbars only detract from the discussion. Simularly for unitarity, or any other mathematical property. Likebox ( talk) 18:48, 1 October 2008 (UTC)
Any usage of natural units is going to confuse the laity, so we should eschew them. I don't see that hbar is any more confusing than just h. -- Michael C. Price talk 15:48, 4 October 2008 (UTC)
I strongly suggest that we include all hbar's (and no h's, for consistency). I agree each symbol is intimidating, but even worse is confusion. People introduced to the schrodinger equation will *not* intuitively understand that by setting hbar=1 you can measure momentum in units of distance. They will just see a massive discrepancy between their textbooks and this page, as well as not understand why the units don't seem to work. Furthermore, it appears someone set m=1 in the section on the green's function, which is an even bigger source of confusion. I do this crap for a living, and I was confused. Njerseyguy ( talk) 06:08, 2 July 2009 (UTC)
Once were done with restoring the hbars, I suggest we tackle on the length and verbosity of this article. There's just too many repetition, the structure is too fine-grained, and many sections go on and on with little benefit to the article. Headbomb { ταλκ κοντριβς – WP Physics} 21:51, 27 February 2010 (UTC)
Alright, since Likebox decided to take his ball and go home, I guess this means we have a mostly clean slate on what to write and how to structure the article. I propose a rough structure that would more or less follow this:
It'll be easier to rewrite this article from scratch, than chase for sources we might not be able to find. Headbomb { ταλκ κοντριβς – WP Physics} 01:46, 1 March 2010 (UTC)
Hi, a new anon editor with an interest in this article noticed my name in the history from a vandal revert and left a message for me regarding this article. Since I only have a basic understanding of quantum physics, I'm really not the best person to deal with it, so I've copied the message here. Wine Guy ~Talk 00:10, 17 March 2010 (UTC)
Copied from User talk:Wine Guy#Revision history of Schrödinger equation. I have seen that a couple of people have suggested an addition to the article that would show the separation of the time-dependent wave function into a product of a time function with a space function, leading to the time-independent form of the Shroedinger equation. This addition would only take a couple of lines, and in my opinion considerably reduce the voodoo factor. Anyone who knows how to take a derivative would follow the logic, even if they had never seen the Schroedinger equation. I hope you will add the needed lines to the article. In the meantime, I will try to learn how to make the changes myself and post it to see if it will be accepted. 76.248.144.40 ( talk) 21:43, 16 March 2010 (UTC)
I am personally embarassed to have an equation that reads:
This is not bad mathematical writing anymore--- it is pure illiteracy. Likebox ( talk) 23:08, 27 February 2010 (UTC)
Where are the sources? Likebox ( talk) 16:36, 28 February 2010 (UTC)
This online software Periodic Potential Lab solves the time independent Schrodinger equation for arbitrary periodic potentials which might be impossible analytically. Does it seem good ides to link it here? ( talk)
It appears to me that all the hbar's are missing in this section, after the following text:
"For the specific case of a single particle in one dimension "
Can somebody confirm please.
Peeter.joot ( talk) 15:39, 1 December 2008 (UTC)
I've added them. Is there a wiki-standard about the use of natural units? -- Michael C. Price talk 11:19, 2 July 2009 (UTC)
The following comment was posted in the Article itself by unidentified user instead of here:
* Density functional theory (need verification, as far as I know, DFT will give you the PDF, from which it is impossible to deduce the wavefunction)
Yours sincerely, GeorgeLouis ( talk) 05:12, 11 July 2009 (UTC)
What part of the derivation do you find controversial--- this is a mathematical text, so unless you discuss, it is impossible to know what you want. Likebox ( talk) 17:08, 26 February 2010 (UTC)
Any person can set hbar = 1 and retrieve
Very few can place the hbar in the correct places of above and retrieve the correct hbarred version
Purge natural units completely from this article, except when natural units are specifically discussed (which really should not be more than mentioning that setting hbar = 1 gives the natural units version). Using natural units completely obfuscates the derivations, and introduces an unnecessary barrier to comprehension. Headbomb { ταλκ κοντριβς – WP Physics} 19:42, 26 February 2010 (UTC)
It's completely unreasonable to expect the average reader to perform this before being able to understand the article. WP:MOSNUM is very clear on this, and for a very good reason, we should write accessibly, for the widest audience possible:
Use familiar units rather than obscure units—do not write over the heads of the readership (e.g., a general-interest topic such as black holes would be best served by having mass expressed in solar masses, but it might be appropriate to use Planck units in an article on the mathematics of black hole evaporation).
The reader is much more poorly served by natural units then without them, and the natural units version of the Schrodinger equation is also far less common. It's trivial to set hbar = 1. It's not trivial to see where the hbars original were. No reader is better served by setting hbar = 1, even if your field of expertise is QM. Headbomb { ταλκ κοντριβς – WP Physics} 20:31, 26 February 2010 (UTC)
(deindent) I wasn't making personal attacks--- I didn't even know you use hbars in life! I thought you just wanted them for the article. Really, nobody who can calculate anything uses hbars, no offense intended.
Again, nearly all theorists beyond the undergraduate level say exactly "E=ω". Experimentalists only don't do that because they need to use engineering units for their devices. Also, nearly all theorists say Δ x Δ p > 1/2. There is no reason to tote around hbars, or to make false distinctions between energy and frequency, between momentum and wavenumber, or between angular momentum and an integer.
The hbar does not come "into play" anywhere--- it is just "1", exactly like the speed of light in relativity. The commutation relations do not need hbar, they are just [x,p]=i. The "hilbert space operators" are trivialities, and every theorist in the world uses natural units.
Irony of ironies: I am surprised that on this page you are arguing Brews ohare's position regarding a fundamental constant. Likebox ( talk) 21:17, 26 February 2010 (UTC)
You two are making the Physics Project a bearpit. I use natural units all the time, but as a computational quantum chemistry, I call them atomic units. However, they should not be used in wikipedia unless we are specifically talking about them. Equations in wikipedia should be such that the student can do a dimension analysis using SI units as a guide. To miss out h-bar is much more confusing. Energy is NOT frequency. So I agree with Headbomb, but he should stop swearing here. -- Bduke (Discussion) 21:40, 26 February 2010 (UTC)
(deindent) The disruption comment was meant to point out the parallels with User:Brews ohare's position on units in Speed of light, and the endless accusations of "disruption" for editors that bring up the issue of fixing the speed of light to be a constant. Fixing hbar to be a constant is no different.
But your proposal is incredibly ridiculous. It will stunt the ability to write every article on quantum mechanics: am I supposed to write
as opposed to the natural
for every single phase factor in a matrix element or in perturbation theory? Are we supposed to duplicate all symbols, using both "p" and "k" for momentum and wavenumber separately? And "w" and "E" for frequency/energy?
Are we supposed to write:
For Feynman diagram integrals? Not only is that silly, it is against all conventions.
To avoid natural units is a waste of letters, and adds a layer of confusion to already confusing topics.
I have a better suggestion, whoever writes the exposition chooses the units. If you've not written any mathematical exposition of quantum mechanics, you have no idea how annoying it is to use engineering units. Likebox ( talk) 00:15, 27 February 2010 (UTC)
This is not a better suggestion. It would merely add confusion. The discussion on this topic is spread between this section and another section further up. Overall, I can see no support for you and several editors supporting the retention of hbar. The consensus is not running your way. I did suggest a compromise, that hbar would be used in all articles likely to attract a readership from undergraduate beginners and allow more complex and advanced articles to change to natural units in advance sections after the introduction. BTW, they are not engineering units; they are science units. It does not help your case to describe the arguments you oppose as "incredibly ridiculous" and "silly". Please assume good faith. My argument regarding beginning approaching the topic is supported recently by another editor in the section further up, and by Headbomb and Michael Price. -- Bduke (Discussion) 04:02, 27 February 2010 (UTC)
(edit conflict) Likebox, how do you know what my experience is? I have been teaching students about the Schrödinger equation for close on 50 years. OK, these have been physical chemistry students, but they are going to come to this article too. It is not just for advanced physics students. It might even be read by someone who left school at 14, but has heard of Schrödinger's cat and wants more information about what Schrödinger did. Look at the contribution above from CosineKitty. That supports my view. My compromise was only about more advanced articles than this one. I do not support using natural units on this article. Headbomb is correct. You do not have consensus for using natural units. You do not seem to understand the use of consensus. You have tried to convince people, as you should to get consensus, but I do not see that you have convinced anyone. Make sure the basic QM articles are free of natural units and then move on. -- Bduke (Discussion) 07:25, 27 February 2010 (UTC)
I am now going to leave it for others to comment. Let us however be quite clear. First, you can not insist on anything here. If you do you are likely to be blocked. Second, you have not persuaded anyone. Third, I may not have edited this article recently, but I can still comment. Indeed I have as much right to do so as you have. In fact I suspect I have been watching this since long before you started on wikipedia. Finally, I am well aware of the use of atomic units. I use them in my research and with postgraduates. I did not use them with second year chemists. Have you any experience with teaching beginners QM from a non-physics background? -- Bduke (Discussion) 08:08, 27 February 2010 (UTC)
(deindent) You see, with this statment, you are simply wrong. You are making the exact same statement that Brews ohare was making regarding the speed of light, that units of time are essentially different from units of space. I have long ago stopped seeing hbar (or c) as a quantity with units, and just like c=1, I think in hbar=1. So that to me, energy and frequency are synonyms, as are momentum and wavenumber (in appropriate context). The idea that the number and type of units we should use is given by god is silly. There are no units--- Quantum Gravity is ultimately dimensionless.13:01, 27 February 2010 (UTC)
(deindent) CosineKitty--- I respect your position--- but I would like to have your opinion after you read the article in depth, and try to understand everything. Superficially it seems that the hbars will help, but I assure you that the opposite is true.
It is not just annoying to do this, it is a matter of bad mathematical writing. I tell you, this is not as an experienced editor, ever since I was 16 years old, if I saw something that wasn't in natural units (like proton mass in MeV/c^2 instead of in MeV) it flashed in bright lights "this was written by an incompetent-- DO NOT READ THIS TEXT". It's a warning sign for a bad physicist, like "It was a dark and stormy night..." and "Bang! Bang! Went the gun!" is a sign of bad writing. I don't want stuff that I wrote to read this way. Likebox ( talk) 20:53, 27 February 2010 (UTC)
Another problem with natural units, that has so far not been mentioned, is that there are several different kinds of natural units. For example, Likebox writes:
while I and every other quantum chemist would write:
using atomic units which gives the energy in Hartrees. This is adding confusion to confusion. The only way is to not use any variety of natural units. -- Bduke (Discussion) 23:46, 27 February 2010 (UTC)
Alright, I went through the article and restored the hbars and the cs. I missed some, one in Schrödinger equation#Historical background and development, one in Schrödinger equation#Nonlinear equation, and one or more in Schrödinger equation#Bra-ket notation because I am unsure of how to unnaturalize them. Please double check my work to make sure I haven't forgotten some in other sections, or made mistakes on the way. Headbomb { ταλκ κοντριβς – WP Physics} 22:20, 27 February 2010 (UTC)
So you are not interested in improving the article? Then what are you doing here on the article's talk page?-- JohnBlackburne words deeds 16:24, 28 February 2010 (UTC)
Likebox, ou keep claiming there is no consensus, when there clearly is as much consensus as one can normally get on an article like this. Your job, as Headbomb says, is to fix the errors, not remove hbar almost everywhere. Those removals were unacceptable. It has been discussed and several editors disagree with you. You are not God. -- Bduke (Discussion) 23:19, 27 February 2010 (UTC)
Having read the whole conversation and article, I feel strongly that we should use hbars everywhere. But the current situation where likebox uses them only in intermediate steps, with links, isn't terrible, and certainly isn't high on the list of the many problems affecting the quality of the article. I would still prefer to change them, but I don't care much.
I am a physicist, I know QFT, I know natural units inside and out. I do hope that everyone who cares about physics will eventually understand the Schrodinger equation and natural units. But we can't teach them both within the same article! Likebox, you seem to have the order backwards: You imply that people should understand how natural units work and then can learn and really understand the Schrodinger equation. That's not how it works in any physics course or textbook I've ever seen or been in or taught. Instead, people learn a bit of quantum mechanics, eventually understand what hbar is and what is the deep connection between energy and frequency, and only then start using natural units. -- Steve ( talk) 01:02, 28 February 2010 (UTC)
moved to Physics page... Chaosdruid ( talk)
This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | Archive 4 |
Paranoidhuman ( talk) 10:29, 14 May 2010 (UTC)
I have seen mentions in the literature of the Schrödinger group in an increasing number of contexts (aging situations, potentials in AdS). I think the article would benefit from some discussion of the group, but I do not know enough about to author a section. —Preceding unsigned comment added by 128.173.125.74 ( talk) 15:33, 13 October 2009 (UTC)
shouldnt the formula where kinetic energy + potential have hbar squared instead of hbar? —Preceding unsigned comment added by 62.136.133.147 ( talk) 13:57, 17 May 2008 (UTC)
Dan Gluck added a subsection to this article making a few spelling mistakes, which Pfalstad corrected. However, there are also a few minor flaws in the content, e.g., particle mass μ of the electron. No electron was mentioned earlier and mass is indicated by M. Before I (or somebody else) correct(s) these minor things, I like to know whether we all agree that this article is the place for Dan's addition. In the list of analytic solutions we find two articles that treat the spherical symmetric problem. If Dan is not satisfied with these two articles, maybe he should improve those. To me Dan's addition seems fairly arbitrary, he could have added to the present article any solution from the list of analytic solutions. Any comments?-- P.wormer 15:24, 22 May 2007 (UTC)
As a professor in physics from Denmark, I am very disappointed, I am concerned because the English written articles have a tendency to penetrate into all other languages. This article has so many errors/misunderstanding that a GA-status will harm the Wikipedia. Quantum mechanics do not need to be presented as something very complicated, and the use of the Dirac's notation is throughout the article completely wrong. Sincerely j.h.povlsen 80.163.26.74 00:36, 13 August 2007 (UTC)
And I emphasize again, that this article does not present the work of Schroedinger, The same article could as well have been about the equations of Heisenberg. The article starts in it's very first equation with a misinterpretation of the Dirac notation, and then it goes on by describing a Complex Hilbert Space. Let me you remind, that Schroedinger was not aware of any of the above mentioned complexities about the world. He was a physicist, and his equation did not just jump out from nothing! He thought, without a thought on Hilbert space, but on the "quantum mechanics" as he knew it at that time. And the quantum mechanics was the discoveries from Planck, Bohr, Luis de Broglie and Einstein. The Planck/Einstein discovery was, that the energy quantization of light/(Electro-magnetic waves) could be expressed as
while Luis de Broglie discovered a relation between momentum and wavelength
In connection with that the energy, according to Newton, consists of a kinetic part and potential part as in
he looked at a monochromatic wave , and realized that the energy could be evaluated as an eigenvalue to
and a momentum component , similarly could be derived as an eigenvalue to
And by inserting this into the Newton energy rule he reached his named equation:
which (in Wikipedia) sadly, seems to become an untold story. I hope some one, some day will tell it. Sincirely j.h.povlsen 80.163.26.74 04:40, 15 August 2007 (UTC)
We can find stationary solutions to the Schrodinger by looking at solutions separable in time and space as: which inserted into the time dependent Schoedinger equation reveal solutions on the form with the time independent part being an eigenfunction to:
where is interpreted as the energy. This equation can be analytically solved for a number of very physical important cases such as the Coulomb potential (orbitals in the hydrogen atom), and the harmonic oscillator (lowest order approximation of arbitrary potential functions around a minimum). "
The quantum mechanics need in a proper formulation to include the classical mechanics in it's macroscopic limit, and the Shroedinger equation does indeed that, as realized by Ehrenfest. Ehrenfest showed from the time dependent Schroedinger equation that the the expectation value , defined as
of a pysical operator (i.e. a Hermetian operator) evolves in time as
where , the Hamiltonian is and denotes the commutator defined as
and by considering the posiotion operator and the momentum operator he derived the correspondance equations
In agreement with Newtons second law.
Sincirely 80.163.26.74 00:01, 17 August 2007 (UTC)j.h.povlsen
From artical
and similarly since: 1: then 2: and hence 3:
I agree with formula 1 and 2 as currently derived however I derive a different answer for formula 3:
So how does this get accounted for? (the problem points are denoted )-- ANONYMOUS COWARD0xC0DE 23:51, 4 September 2007 (UTC)
Someone should go back through this article and change the sloppy notation for the wavefunction Psi. Psi is a function of x and t, while psi is one a function of x. This can wildly confuse a physicist or student looking for mathemetical expressions described by the Schrodinger Equation. Perhaps putting the wavefunction in the form of its variables Psi(x,t) and psi(x) can alleviate this confusion. —Preceding unsigned comment added by GaiaMind ( talk • contribs) 05:29, 28 October 2007 (UTC)
Referring to the state vector as "one dimensional" is misleading; it is typically infinite dimensional Peter1c 07:29, 7 November 2007 (UTC)
In order to uphold the quality of Wikipedia:Good articles, all articles listed as Good articles are being reviewed against the GA criteria as part of the GA project quality task force. While all the hard work that has gone into this article is appreciated, unfortunately, as of February 15, 2008, this article fails to satisfy the criteria, as detailed below. For that reason, the article has been delisted from WP:GA. However, if improvements are made bringing the article up to standards, the article may be nominated at WP:GAN. If you feel this decision has been made in error, you may seek remediation at WP:GAR. I've had to delist this article from GA status as part of the good article quality control sweeps. It lacks inline references which became a good article requirement in 2006, possibly after this article was passed. I've listed this article at our unreferenced good article task force. Once adequate inline sources have been added, hopefully the article can easily reattain GA status. -- jwanders Talk 12:26, 15 February 2008 (UTC)
I am in the process of cleaning up the article via my sandbox version. Feel free to comment on it. Thanks. MP ( talk• contribs) 12:14, 17 February 2008 (UTC)
Upon request, I've just rewritten the article with my sandbox version. A lot more work still needs to be done though. MP ( talk• contribs) 17:09, 8 March 2008 (UTC)
I decided to remove the subsections Schrodinger wave equation and wave function as I think there is no point in repeating what's already been said in the article and a lot of the stuff will not help to actually understand the Schrodinger equation per se. Hope this is ok; comments/criticisms welcome. Thanks. MP ( talk• contribs) 06:53, 14 March 2008 (UTC)
I've always seen the time-dependent wavefunction written with a capital psi and the time-independent function with a lowercase one, e.g. . It took me a moment to work out what the article was talking about as a result. Is there a particular notation used by most physicists, or was my physics textbook just using an unconventional convention (so to speak)? — Xaonon ( Talk) 19:37, 27 March 2008 (UTC)
Is it really necessary to add 'citation needed' 3-4 times per sentence? It's unreadable. Put a sentence in the beginning to give a conceptual (useless) description, then give the math for people who want to know. To paraphrase Lord Kelvin, if you cannot quantify it, you don't know what you're talking about. —Preceding unsigned comment added by 70.249.215.163 ( talk) 22:58, 27 March 2008 (UTC)
this article is too complex to be comprehended by general public. this article presume the reader to have an advanced understading and knowledge in the subject. a less mathematical approach, a more conceptual approach is required for people who have limited knowledge in physics and mathematics. I suggests to remove the more complex parts from this page into a new article. So that it would be possible for general reader to understand this subject. —The preceding unsigned comment was added by 202.152.240.246 ( talk) 15:22, 2 May 2007 (UTC).
I dissagree with the wording that an electron is a microscopic paricle, its smaller than that! Noosentaal ( talk) 17:53, 7 April 2008 (UTC)
I think that one should not present pseudo-history as history. It is possible to give modern mathematical derivations, but in a historical discussion I think it is good to stick to the actual events, if not the exact formulas. Likebox ( talk) 02:44, 15 May 2008 (UTC)
Too much detail is just as bad as too little. The person who is reading this page should be able to reproduce elementary algebraic manipulations. Likebox ( talk) 21:58, 15 May 2008 (UTC)
(deindent) Maybe you're right, I am not so great with psychology. But I think that the previous argument was essentially identical, except it was done with more detail to make the algebraic steps more explicit. The issue I had with that (and I might be psychologically totally off base here) is that I think it makes the reader lose the forest for the trees. It had many equations whose only purpose was to restate the equivalence of E and \omega and p and k. By doing this, a larger fraction of the "steps" are easier to follow, but only because the number of steps is made larger by including more algebraic restatements of p=hk. So, it would say "p=hk" and later "k=i d/dx \psi" and later "p=i\hbar d/dx". This sort of thing bothered me when I was a student (At least I think I remember that it did) because it would obscure the essentially new insights--- in this case the substitution of derivative operators in the energy equation--- by hiding them among a list of algebraic manipulations which should be internalized by the reader first, before doing anything else. But perhaps its the exact opposite. Maybe if there are more familiar identities, there is a feeling of familiarity which aids the process of understanding.
The group-velocity stuff might be an unnecessary hurdle for a first read, and it might need to be removed. You might also be right that a careful restatement of p=hk multiple times will reinforce understanding, because different people might "click" on different restatements. I have no confidence that the current version is any good at all. The previous presentation might be significantly better. Probably this is best figured out by asking some students who have just finished learning quantum mechanics.
About Schrodinger and Copenhagen--- I read conflicting stuff on this. Everybody agrees that at first, he hated the Copenhagen interpretation, and thought \psi was a physical charge density or something, but after Born's paper he (and Einstein and everyone else) came to agree that, given the formalism, a statistical interpretation is the only sensible one. The question that remains is whether he held out hope that this was a statistical approximation to an underlying determinisic DeBroglie-Bohm theory, or if he had some Wigneresque proto-Everettist ideas. This I don't know for sure. In the new Einstein biography by Isaacson, the author states that Schrodinger was sympathetic to Einstein's view at least up to EPR, but in the 1940s goes on a rant to someone or other about how Einstein was a stupid old man when it came to quantum mechanics. That's why I assumed he had come to accept that the Copenhagen interpretation is correct. If you have better information, please fix it. I don't have any insight into Schrodinger's thinking. Likebox ( talk) 20:14, 18 May 2008 (UTC)
"Schrödinger tried unsuccessfully to interpret it as a charge density." This is a very interesting claim! In the history of relativistic QM, it is well known that the Klein-Gordon equation was originally discarded because its wavefunction failed to fit the probability interpretation. BUT! In modern QFT, the Klein-Gordon equation is actually correct -- the wavefunction just has to be interpreted as charge density rather than probability. So if Schroedinger really started out interpreting the wavefunction as charge density, and considering that he also preceded Klein and Gordon by trying that equation before trying the one he is now known for, surely there is more interesting history worth telling here (or at least, the Klein-Gordon page needs a better history section). Cesiumfrog ( talk) 05:01, 31 May 2008 (UTC)
There is a difference between believing that the Copenhagen interpretation is incorrect or incomplete and believing that the statistical interpretation of the wavefunction is incorrect. While I don't know for sure whether Schrodinger believed that the Copenhagen interpretation was a final statement on the nature of physical reality, I am sure that, like Einstein and everybody else, he accepted Born's analysis as correct and realized that the wavefunction could only be interpreted as a probability. This was a universal conclusion, everyone agreed with Born's interpretation. For example, Einstein is directly quoted in Isaacson as saying that the only possible interpretation of the wavefunction is statistical, that this is an unavoidable conclusion. This was (and still is) such a clear fact that I can't imagine Schrodinger rejected it. He certainly understood, although I'm sure with distaste, that the probability is proportional to the wavefunction squared (although perhaps with a philosophy radically different than those that were codified by Bohr). His often quoted dislike of quantum discontinuities should be properly read as a sign that he initially wanted to avoid all quantum jumps with a continuous wave formalism, but failed. I don't have any insight into whether he thought that quantum mechanics was a statistical approximation to a deeper underlying theory. Likebox ( talk) 00:17, 20 May 2008 (UTC)
This article has undergone a major sequence of changes, the second last (before my revert) of which (by an anon.) completely obliterated crucial info. on the forms of the Schrodinger equation, but kept a mass of mathematical detail that is not relevant to the article or point being made at hand. I intend to sort out this article at some point. There is too much maths which could - and should - be moved to articles dealing with those issues more directly. MP ( talk• contribs) 18:44, 13 June 2008 (UTC)
The section "nondegenerate ground state" contains an incorrect proof that the ground state of a Schrodinger equation is a nonnegative function and nondegenerate. A while ago the proof was replaced by a better one but then reverted back.
I located this wikipedia article while looking for a proof of this well known property. While it is not clear whether the proof belongs here in this article, let me first say why the proof as it stands is wrong.
The proof is based on the variational principle. The proof shown currently is that if is a test function that changes sign and minimizes the energy functional then we can take as another test function that has the same integrals of potential and kinetic energy, except for the kink at the place where . The kink should then be smoothed out, and the result is that we now have a test function that has a smaller value of the energy functional. This contradiction proves the statement.
This is incorrect because it's not true that we can always straighten the kink while not increasing the energy functional. An easy counterexample is and . The kinetic energy of this is identically zero, so . If we now take and straighten the kink, the kinetic energy is going to be strictly positive no matter how smoothly we straighten it. So the new test function has always a strictly greater value of the energy functional. This counterexample shows that it is not possible to smooth the kink as required.
The proof that was deleted by an edit on 31 August was better: it allowed a small increase of the energy functional while straightening the kink.
I'd like some experts in mathematical physics to examine this argument. In my view the proof of this important statement needs to be either presented clearly and correctly, or removed and replaced by a reference to a textbook. Sznagy ( talk) 14:35, 9 & 13:52, 11 September 2008
The problem with all the hbars is that for a new person, each symbol is intimidating. The fewer symbols the better. In this case, the constant is only performing a unit conversion, and so should not be included except:
When talking about abstract theorems, like the positivity of the ground state wavefunction, the hbars only detract from the discussion. Simularly for unitarity, or any other mathematical property. Likebox ( talk) 18:48, 1 October 2008 (UTC)
Any usage of natural units is going to confuse the laity, so we should eschew them. I don't see that hbar is any more confusing than just h. -- Michael C. Price talk 15:48, 4 October 2008 (UTC)
I strongly suggest that we include all hbar's (and no h's, for consistency). I agree each symbol is intimidating, but even worse is confusion. People introduced to the schrodinger equation will *not* intuitively understand that by setting hbar=1 you can measure momentum in units of distance. They will just see a massive discrepancy between their textbooks and this page, as well as not understand why the units don't seem to work. Furthermore, it appears someone set m=1 in the section on the green's function, which is an even bigger source of confusion. I do this crap for a living, and I was confused. Njerseyguy ( talk) 06:08, 2 July 2009 (UTC)
Once were done with restoring the hbars, I suggest we tackle on the length and verbosity of this article. There's just too many repetition, the structure is too fine-grained, and many sections go on and on with little benefit to the article. Headbomb { ταλκ κοντριβς – WP Physics} 21:51, 27 February 2010 (UTC)
Alright, since Likebox decided to take his ball and go home, I guess this means we have a mostly clean slate on what to write and how to structure the article. I propose a rough structure that would more or less follow this:
It'll be easier to rewrite this article from scratch, than chase for sources we might not be able to find. Headbomb { ταλκ κοντριβς – WP Physics} 01:46, 1 March 2010 (UTC)
Hi, a new anon editor with an interest in this article noticed my name in the history from a vandal revert and left a message for me regarding this article. Since I only have a basic understanding of quantum physics, I'm really not the best person to deal with it, so I've copied the message here. Wine Guy ~Talk 00:10, 17 March 2010 (UTC)
Copied from User talk:Wine Guy#Revision history of Schrödinger equation. I have seen that a couple of people have suggested an addition to the article that would show the separation of the time-dependent wave function into a product of a time function with a space function, leading to the time-independent form of the Shroedinger equation. This addition would only take a couple of lines, and in my opinion considerably reduce the voodoo factor. Anyone who knows how to take a derivative would follow the logic, even if they had never seen the Schroedinger equation. I hope you will add the needed lines to the article. In the meantime, I will try to learn how to make the changes myself and post it to see if it will be accepted. 76.248.144.40 ( talk) 21:43, 16 March 2010 (UTC)
I am personally embarassed to have an equation that reads:
This is not bad mathematical writing anymore--- it is pure illiteracy. Likebox ( talk) 23:08, 27 February 2010 (UTC)
Where are the sources? Likebox ( talk) 16:36, 28 February 2010 (UTC)
This online software Periodic Potential Lab solves the time independent Schrodinger equation for arbitrary periodic potentials which might be impossible analytically. Does it seem good ides to link it here? ( talk)
It appears to me that all the hbar's are missing in this section, after the following text:
"For the specific case of a single particle in one dimension "
Can somebody confirm please.
Peeter.joot ( talk) 15:39, 1 December 2008 (UTC)
I've added them. Is there a wiki-standard about the use of natural units? -- Michael C. Price talk 11:19, 2 July 2009 (UTC)
The following comment was posted in the Article itself by unidentified user instead of here:
* Density functional theory (need verification, as far as I know, DFT will give you the PDF, from which it is impossible to deduce the wavefunction)
Yours sincerely, GeorgeLouis ( talk) 05:12, 11 July 2009 (UTC)
What part of the derivation do you find controversial--- this is a mathematical text, so unless you discuss, it is impossible to know what you want. Likebox ( talk) 17:08, 26 February 2010 (UTC)
Any person can set hbar = 1 and retrieve
Very few can place the hbar in the correct places of above and retrieve the correct hbarred version
Purge natural units completely from this article, except when natural units are specifically discussed (which really should not be more than mentioning that setting hbar = 1 gives the natural units version). Using natural units completely obfuscates the derivations, and introduces an unnecessary barrier to comprehension. Headbomb { ταλκ κοντριβς – WP Physics} 19:42, 26 February 2010 (UTC)
It's completely unreasonable to expect the average reader to perform this before being able to understand the article. WP:MOSNUM is very clear on this, and for a very good reason, we should write accessibly, for the widest audience possible:
Use familiar units rather than obscure units—do not write over the heads of the readership (e.g., a general-interest topic such as black holes would be best served by having mass expressed in solar masses, but it might be appropriate to use Planck units in an article on the mathematics of black hole evaporation).
The reader is much more poorly served by natural units then without them, and the natural units version of the Schrodinger equation is also far less common. It's trivial to set hbar = 1. It's not trivial to see where the hbars original were. No reader is better served by setting hbar = 1, even if your field of expertise is QM. Headbomb { ταλκ κοντριβς – WP Physics} 20:31, 26 February 2010 (UTC)
(deindent) I wasn't making personal attacks--- I didn't even know you use hbars in life! I thought you just wanted them for the article. Really, nobody who can calculate anything uses hbars, no offense intended.
Again, nearly all theorists beyond the undergraduate level say exactly "E=ω". Experimentalists only don't do that because they need to use engineering units for their devices. Also, nearly all theorists say Δ x Δ p > 1/2. There is no reason to tote around hbars, or to make false distinctions between energy and frequency, between momentum and wavenumber, or between angular momentum and an integer.
The hbar does not come "into play" anywhere--- it is just "1", exactly like the speed of light in relativity. The commutation relations do not need hbar, they are just [x,p]=i. The "hilbert space operators" are trivialities, and every theorist in the world uses natural units.
Irony of ironies: I am surprised that on this page you are arguing Brews ohare's position regarding a fundamental constant. Likebox ( talk) 21:17, 26 February 2010 (UTC)
You two are making the Physics Project a bearpit. I use natural units all the time, but as a computational quantum chemistry, I call them atomic units. However, they should not be used in wikipedia unless we are specifically talking about them. Equations in wikipedia should be such that the student can do a dimension analysis using SI units as a guide. To miss out h-bar is much more confusing. Energy is NOT frequency. So I agree with Headbomb, but he should stop swearing here. -- Bduke (Discussion) 21:40, 26 February 2010 (UTC)
(deindent) The disruption comment was meant to point out the parallels with User:Brews ohare's position on units in Speed of light, and the endless accusations of "disruption" for editors that bring up the issue of fixing the speed of light to be a constant. Fixing hbar to be a constant is no different.
But your proposal is incredibly ridiculous. It will stunt the ability to write every article on quantum mechanics: am I supposed to write
as opposed to the natural
for every single phase factor in a matrix element or in perturbation theory? Are we supposed to duplicate all symbols, using both "p" and "k" for momentum and wavenumber separately? And "w" and "E" for frequency/energy?
Are we supposed to write:
For Feynman diagram integrals? Not only is that silly, it is against all conventions.
To avoid natural units is a waste of letters, and adds a layer of confusion to already confusing topics.
I have a better suggestion, whoever writes the exposition chooses the units. If you've not written any mathematical exposition of quantum mechanics, you have no idea how annoying it is to use engineering units. Likebox ( talk) 00:15, 27 February 2010 (UTC)
This is not a better suggestion. It would merely add confusion. The discussion on this topic is spread between this section and another section further up. Overall, I can see no support for you and several editors supporting the retention of hbar. The consensus is not running your way. I did suggest a compromise, that hbar would be used in all articles likely to attract a readership from undergraduate beginners and allow more complex and advanced articles to change to natural units in advance sections after the introduction. BTW, they are not engineering units; they are science units. It does not help your case to describe the arguments you oppose as "incredibly ridiculous" and "silly". Please assume good faith. My argument regarding beginning approaching the topic is supported recently by another editor in the section further up, and by Headbomb and Michael Price. -- Bduke (Discussion) 04:02, 27 February 2010 (UTC)
(edit conflict) Likebox, how do you know what my experience is? I have been teaching students about the Schrödinger equation for close on 50 years. OK, these have been physical chemistry students, but they are going to come to this article too. It is not just for advanced physics students. It might even be read by someone who left school at 14, but has heard of Schrödinger's cat and wants more information about what Schrödinger did. Look at the contribution above from CosineKitty. That supports my view. My compromise was only about more advanced articles than this one. I do not support using natural units on this article. Headbomb is correct. You do not have consensus for using natural units. You do not seem to understand the use of consensus. You have tried to convince people, as you should to get consensus, but I do not see that you have convinced anyone. Make sure the basic QM articles are free of natural units and then move on. -- Bduke (Discussion) 07:25, 27 February 2010 (UTC)
I am now going to leave it for others to comment. Let us however be quite clear. First, you can not insist on anything here. If you do you are likely to be blocked. Second, you have not persuaded anyone. Third, I may not have edited this article recently, but I can still comment. Indeed I have as much right to do so as you have. In fact I suspect I have been watching this since long before you started on wikipedia. Finally, I am well aware of the use of atomic units. I use them in my research and with postgraduates. I did not use them with second year chemists. Have you any experience with teaching beginners QM from a non-physics background? -- Bduke (Discussion) 08:08, 27 February 2010 (UTC)
(deindent) You see, with this statment, you are simply wrong. You are making the exact same statement that Brews ohare was making regarding the speed of light, that units of time are essentially different from units of space. I have long ago stopped seeing hbar (or c) as a quantity with units, and just like c=1, I think in hbar=1. So that to me, energy and frequency are synonyms, as are momentum and wavenumber (in appropriate context). The idea that the number and type of units we should use is given by god is silly. There are no units--- Quantum Gravity is ultimately dimensionless.13:01, 27 February 2010 (UTC)
(deindent) CosineKitty--- I respect your position--- but I would like to have your opinion after you read the article in depth, and try to understand everything. Superficially it seems that the hbars will help, but I assure you that the opposite is true.
It is not just annoying to do this, it is a matter of bad mathematical writing. I tell you, this is not as an experienced editor, ever since I was 16 years old, if I saw something that wasn't in natural units (like proton mass in MeV/c^2 instead of in MeV) it flashed in bright lights "this was written by an incompetent-- DO NOT READ THIS TEXT". It's a warning sign for a bad physicist, like "It was a dark and stormy night..." and "Bang! Bang! Went the gun!" is a sign of bad writing. I don't want stuff that I wrote to read this way. Likebox ( talk) 20:53, 27 February 2010 (UTC)
Another problem with natural units, that has so far not been mentioned, is that there are several different kinds of natural units. For example, Likebox writes:
while I and every other quantum chemist would write:
using atomic units which gives the energy in Hartrees. This is adding confusion to confusion. The only way is to not use any variety of natural units. -- Bduke (Discussion) 23:46, 27 February 2010 (UTC)
Alright, I went through the article and restored the hbars and the cs. I missed some, one in Schrödinger equation#Historical background and development, one in Schrödinger equation#Nonlinear equation, and one or more in Schrödinger equation#Bra-ket notation because I am unsure of how to unnaturalize them. Please double check my work to make sure I haven't forgotten some in other sections, or made mistakes on the way. Headbomb { ταλκ κοντριβς – WP Physics} 22:20, 27 February 2010 (UTC)
So you are not interested in improving the article? Then what are you doing here on the article's talk page?-- JohnBlackburne words deeds 16:24, 28 February 2010 (UTC)
Likebox, ou keep claiming there is no consensus, when there clearly is as much consensus as one can normally get on an article like this. Your job, as Headbomb says, is to fix the errors, not remove hbar almost everywhere. Those removals were unacceptable. It has been discussed and several editors disagree with you. You are not God. -- Bduke (Discussion) 23:19, 27 February 2010 (UTC)
Having read the whole conversation and article, I feel strongly that we should use hbars everywhere. But the current situation where likebox uses them only in intermediate steps, with links, isn't terrible, and certainly isn't high on the list of the many problems affecting the quality of the article. I would still prefer to change them, but I don't care much.
I am a physicist, I know QFT, I know natural units inside and out. I do hope that everyone who cares about physics will eventually understand the Schrodinger equation and natural units. But we can't teach them both within the same article! Likebox, you seem to have the order backwards: You imply that people should understand how natural units work and then can learn and really understand the Schrodinger equation. That's not how it works in any physics course or textbook I've ever seen or been in or taught. Instead, people learn a bit of quantum mechanics, eventually understand what hbar is and what is the deep connection between energy and frequency, and only then start using natural units. -- Steve ( talk) 01:02, 28 February 2010 (UTC)
moved to Physics page... Chaosdruid ( talk)
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