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It seems, position-space and momentum-space wave functions are normalized, but others are not; and every linear combination of wave functions is a wave function... a mess? Boris Tsirelson ( talk) 14:26, 30 April 2016 (UTC)
On one hand, it is nice to pin down all mathematical and physical properties/requirements first thing (after the history).
On the other hand, it would be easier for typical readers to just see what the wave function is with examples, and the mathematical details later. Also, since the probability interpretation is what most sources present that section could be moved further up. The Hydrogen atom content in the function spaces section has been moved to the section of that example.
I tried to rearrange to see how it looks, and will not make further edits. Anyone is free to revert if they disagree. M ∧Ŝ c2ħε Иτlk 06:50, 3 May 2016 (UTC)
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Cheers.— cyberbot II Talk to my owner:Online 20:17, 26 May 2016 (UTC)
Is wavefunction (one word) now a word? (I note that the spell checker/corrector on my browser believes it is two words.) I note that there is a redirect from the one word form, but, even more, it is used in many articles. Gah4 ( talk) 23:40, 17 January 2017 (UTC)
Subsection Wave function#Particle in a box is created by Maschen in 2014 by moving the content from "normalization example". However, the "normalization example" was just about normalization, it did not mention any potential, while Particle in a box is about potential infinite outside the box, and stipulates the corresponding boundary conditions (leading to discrete spectrum). So, this subsection is unsatisfactory (since 2014 till now). Boris Tsirelson ( talk) 17:07, 2 May 2017 (UTC)
There is something called "Box Normalization" that is frequently used, and has little (but still something) to do with "Particle in Box" (no potential). The effect is quantization of momentum, and a normalization is possible within the (very large) box. YohanN7 ( talk) 08:05, 28 June 2017 (UTC) Discussed here. YohanN7 ( talk) 08:09, 28 June 2017 (UTC)
The phase of a wave function can be represented by a continuum of different colors. The probability density can be represented by the intensity of the color. In this way we can give full information about any 2D wave function. There is a problem of contrast. If the probability density of one part of the image is too little than the one on another part, it won't be seen. But there is a simple solution : the intensity of the color shall depend logarithmically, not linearly, on the probability density. This is a mistake I made in my previous animations (linear dependence, not logarithmic). I just thought about it. I will make use of this thought in my future animations. I hope also that others will make use of this idea. With it we can visualize many quantum wave functions. TD ( talk) 08:51, 16 August 2023 (UTC)
@ EditingPencil I'm not sure if I agree with the use of proper vectors and improper vectors. They are effectively eigenfunctions according to the source you cite (on page 67), but with respect to (what the author calls) a "physical" Hilbert space. Apart from the fact that this type of Hilber space hasn't been introduced, I also think it's better to refer to them as eigenfunctions as that's much more conventional. The subsection Eigenvalues and eigenfunctions of Hermitian operators clarifies its use in continuous settings and cites a good source as well. Roffaduft ( talk) 07:02, 16 November 2023 (UTC)
""physical" Hilbert space comes from a postulate of QM, here"
However, the term is often used nowadays, as in these notes, in a way that includes finite-dimensional spaces, namely:
finite-dimensional Hilbert space.
This
level-4 vital article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||
|
Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
pageviews.wmcloud.org |
The contents of the Normalizable wave function page were merged into Wave function on January 2012. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
Text and/or other creative content from Normalizable wave function was copied or moved into wave function with this edit. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
This page has archives. Sections older than 90 days may be automatically archived by Lowercase sigmabot III when more than 3 sections are present. |
It seems, position-space and momentum-space wave functions are normalized, but others are not; and every linear combination of wave functions is a wave function... a mess? Boris Tsirelson ( talk) 14:26, 30 April 2016 (UTC)
On one hand, it is nice to pin down all mathematical and physical properties/requirements first thing (after the history).
On the other hand, it would be easier for typical readers to just see what the wave function is with examples, and the mathematical details later. Also, since the probability interpretation is what most sources present that section could be moved further up. The Hydrogen atom content in the function spaces section has been moved to the section of that example.
I tried to rearrange to see how it looks, and will not make further edits. Anyone is free to revert if they disagree. M ∧Ŝ c2ħε Иτlk 06:50, 3 May 2016 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Wave function. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{
Sourcecheck}}
).
An editor has reviewed this edit and fixed any errors that were found.
Cheers.— cyberbot II Talk to my owner:Online 20:17, 26 May 2016 (UTC)
Is wavefunction (one word) now a word? (I note that the spell checker/corrector on my browser believes it is two words.) I note that there is a redirect from the one word form, but, even more, it is used in many articles. Gah4 ( talk) 23:40, 17 January 2017 (UTC)
Subsection Wave function#Particle in a box is created by Maschen in 2014 by moving the content from "normalization example". However, the "normalization example" was just about normalization, it did not mention any potential, while Particle in a box is about potential infinite outside the box, and stipulates the corresponding boundary conditions (leading to discrete spectrum). So, this subsection is unsatisfactory (since 2014 till now). Boris Tsirelson ( talk) 17:07, 2 May 2017 (UTC)
There is something called "Box Normalization" that is frequently used, and has little (but still something) to do with "Particle in Box" (no potential). The effect is quantization of momentum, and a normalization is possible within the (very large) box. YohanN7 ( talk) 08:05, 28 June 2017 (UTC) Discussed here. YohanN7 ( talk) 08:09, 28 June 2017 (UTC)
The phase of a wave function can be represented by a continuum of different colors. The probability density can be represented by the intensity of the color. In this way we can give full information about any 2D wave function. There is a problem of contrast. If the probability density of one part of the image is too little than the one on another part, it won't be seen. But there is a simple solution : the intensity of the color shall depend logarithmically, not linearly, on the probability density. This is a mistake I made in my previous animations (linear dependence, not logarithmic). I just thought about it. I will make use of this thought in my future animations. I hope also that others will make use of this idea. With it we can visualize many quantum wave functions. TD ( talk) 08:51, 16 August 2023 (UTC)
@ EditingPencil I'm not sure if I agree with the use of proper vectors and improper vectors. They are effectively eigenfunctions according to the source you cite (on page 67), but with respect to (what the author calls) a "physical" Hilbert space. Apart from the fact that this type of Hilber space hasn't been introduced, I also think it's better to refer to them as eigenfunctions as that's much more conventional. The subsection Eigenvalues and eigenfunctions of Hermitian operators clarifies its use in continuous settings and cites a good source as well. Roffaduft ( talk) 07:02, 16 November 2023 (UTC)
""physical" Hilbert space comes from a postulate of QM, here"
However, the term is often used nowadays, as in these notes, in a way that includes finite-dimensional spaces, namely:
finite-dimensional Hilbert space.