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User Papa November asked for so comments and feedback.
My primary observation is that this article focuses why to much on explaining how to solve the particle-in-a-box problem in quantum mechanics. Please bear in mind that wikipedia is not a textbooks or a how to guide. As it stands the article reads like a couple of pages from an undergrad physics textbook, not an encyclopedia article. To make the article more encyclopedic I suggest:
Finally, a word of general advice when writting physics articles. Try not to think too much like a physicist, but try to view the text from the perspective of a layman. ( TimothyRias ( talk) 09:43, 4 September 2009 (UTC))
Hi Chhe, please could you clarify a point about your comments? Are you saying that the article (in its current state) needs to have a more detailed derivation or that it's OK as it is? I've tried to strike a balance so that the article is easy for the layman to read and gain some understanding of the topic, while still keeping all the important points of the derivation. Ideally, there should be enough information for mathematically-competent readers to fully understand how the solution was obtained, but not enough to exclude the layman. The important point, I think, is that this is an encyclopaedia article rather than a textbook or a teaching guide. If the advanced reader wants a really rigorous mathematical derivation then we can easily cite a reference which provides this. Papa November ( talk) 12:59, 9 February 2010 (UTC)
The section on the three-dimensional case says when two or more of the lengths are the same (e.g. Lx = Ly), there are multiple wavefunctions corresponding to the same total energy. That's true in two dimensions too. The two-dimensional case is discussed first, and doesn't mention this, making it seem as though it first comes up in three dimensions. —Preceding unsigned comment added by 72.75.67.226 ( talk) 03:48, 8 October 2009 (UTC)
In the caption for the energy dispersion diagram, I believe the expression kn=2π/L should read kn=nπ/L. The reason I say this is that kn implies "k as a function of n," and yet there is no "n" in the formula. Otherwise this was an article good enough to discuss with my Adv. Inorganic students, and it was nice having access to this information online. Keep up the good work. Rowanw3 ( talk) 21:20, 24 November 2009 (UTC)
The author makes the following assertion:
For the particle in a box, it can be shown that the average position is always <x> = L/2, regardless of the state of the particle.
The above statement is only true if the expectation is taken for an eigenstate. However, the most general state of a particle in a box is a linear combination of eigenstates. For such a general state the expectation value will not always be L/2. See for instance http://en.citizendium.org/wiki/Particle_in_a_box for a graphic demonstration.
PsiStar ( talk) 21:13, 2 March 2011 (UTC)
Dear Author, The formula for energy levels in higher dimensions seems to be wrong. For the two dimensional equation it states currently: E_nx,ny = h^2/2m (k_nx + k_ny)^2 = h^2/2m (n_x pi/L_x + n_y pi/L_y)^2. But it should read instead: E_nx,ny = h^2/2m (k_nx^2 + k_ny^2) = h^2/2m ((n_x pi/L_x)^2 + (n_y pi/L_y)^2). As the eigenvalues of the 2D-Laplacian are 2,5,5,8,10 ... = (1+1),(1+4),(4+1),(4+4),(1+9) ... The same applies to the three dimensional equation. Please verify and correct this. — Preceding unsigned comment added by Pia novice ( talk • contribs) 23:11, 22 February 2012 (UTC)
If the boundary conditions are changed from "x=0 to x=L" to "x=-L/2 & x=+L/2", how to find the two constants A & B. Since in this case none of the constants goes to zero. — Preceding unsigned comment added by Imrohit2611 ( talk • contribs) 09:12, 14 April 2018 (UTC)
The derivation in the article is largely centered around the time-dependent SE, yet a discussion of the discrete stationary states is mixed into the text, without any mention that those are solutions of the time-independent SE. The effect must be thoroughly confusing to anyone who doesn't firmly master Quantum Mechanics but has a serious interest in learning more about it (presumably our target audience).
I would suggest to dedicate an equal amount of space to the time-independent and time-dependent solutions, each under their respective subheadings.
I'm tempted to put a Cleanup template on top based on this issue alone (and there are more on this page).
OneAhead (
talk)
14:25, 8 April 2020 (UTC)
@ Luman2009: I'm not a physicist, so I apologize if I'm totally wrong here. Is the material in the new section "A more general analytically solvable problem in quantum mechanics" explicitly supported by the sources? As a layman, it seems to me like it might be original research, so I wanted to double-check. BalinKingOfMoria ( talk) 02:11, 22 August 2022 (UTC)
@
Luman2009: Discussion about
Kronig-Penney type of model does not belong to this article. This article is about an infinite potential well. If you make multiple copies of infinite potential wells, you do not get any band dispersion, as the electronic states in the wells are completely independent of each other. I have removed the content.
Jähmefyysikko (
talk)
11:37, 24 July 2023 (UTC)
The above text that has been striken out was based on the misunderstanding of the model. New try: So the model is an infinite potential well with additional priodic potential inside the well. I think it is too far removed from the original model to be discussed here. Jähmefyysikko ( talk) 11:41, 24 July 2023 (UTC)
The infinite potential well with Dirichlet boundary isn't a physical model, and furthermore fails to present a consistent quantum mechanical system, due to the bad domain of definition of with the chosen boundary conditions. Some sources:
https://link.springer.com/book/10.1007/978-1-4614-7116-5 Ch 9.6 "A Counterexample" (ominous),
https://courses.physics.illinois.edu/phys508/fa2017/amaster.pdf Section 4.2.4 (speedy overview), and
https://arxiv.org/abs/quant-ph/0103153 2 "The infinite potential well : paradoxes"
This last paper makes the following observation regarding the Hamiltonian operator and its square:
With state vector (on the interval), we have , and attempts to measure the squared energy yield either:
where are even energy eigenvalues, versus
. Disaster.
It all comes down to the spectral theory: The construction given with boundary conditions is a space where the momentum operator fails to be an essentially self-adjoint operator, after this everything falls apart. One can only resolve this by modifying the wave function space, with twisted periodic boundary conditions for some to be decided. The intuition that is wrong, and perhaps fails us here because the potential is infinite. A better intuition is that our wave functions should start in , and position eigenvectors may end up being continuous under constraint by the system.
Of course, this particular particle-in-a-box is still a useful model to study in the beginning, which creates a tension. But surely the fact that the derivation leads to contradictions, enforces bad intuitions, obscures the free variable and the physically relevant twisted boundary, and is fundamentally incompatible with the underlying theory should be signposted somewhere for readers. There seem to be a lot of misconceptions out there regarding these questions, and this is a fundamental example in the pedagogy. Jagmanjg ( talk) 09:36, 19 March 2024 (UTC)
This is the
talk page for discussing improvements to the
Particle in a box article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
Archives: 1 |
![]() | Particle in a box was a good articles nominee, but did not meet the good article criteria at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake. | |||||||||
|
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
User Papa November asked for so comments and feedback.
My primary observation is that this article focuses why to much on explaining how to solve the particle-in-a-box problem in quantum mechanics. Please bear in mind that wikipedia is not a textbooks or a how to guide. As it stands the article reads like a couple of pages from an undergrad physics textbook, not an encyclopedia article. To make the article more encyclopedic I suggest:
Finally, a word of general advice when writting physics articles. Try not to think too much like a physicist, but try to view the text from the perspective of a layman. ( TimothyRias ( talk) 09:43, 4 September 2009 (UTC))
Hi Chhe, please could you clarify a point about your comments? Are you saying that the article (in its current state) needs to have a more detailed derivation or that it's OK as it is? I've tried to strike a balance so that the article is easy for the layman to read and gain some understanding of the topic, while still keeping all the important points of the derivation. Ideally, there should be enough information for mathematically-competent readers to fully understand how the solution was obtained, but not enough to exclude the layman. The important point, I think, is that this is an encyclopaedia article rather than a textbook or a teaching guide. If the advanced reader wants a really rigorous mathematical derivation then we can easily cite a reference which provides this. Papa November ( talk) 12:59, 9 February 2010 (UTC)
The section on the three-dimensional case says when two or more of the lengths are the same (e.g. Lx = Ly), there are multiple wavefunctions corresponding to the same total energy. That's true in two dimensions too. The two-dimensional case is discussed first, and doesn't mention this, making it seem as though it first comes up in three dimensions. —Preceding unsigned comment added by 72.75.67.226 ( talk) 03:48, 8 October 2009 (UTC)
In the caption for the energy dispersion diagram, I believe the expression kn=2π/L should read kn=nπ/L. The reason I say this is that kn implies "k as a function of n," and yet there is no "n" in the formula. Otherwise this was an article good enough to discuss with my Adv. Inorganic students, and it was nice having access to this information online. Keep up the good work. Rowanw3 ( talk) 21:20, 24 November 2009 (UTC)
The author makes the following assertion:
For the particle in a box, it can be shown that the average position is always <x> = L/2, regardless of the state of the particle.
The above statement is only true if the expectation is taken for an eigenstate. However, the most general state of a particle in a box is a linear combination of eigenstates. For such a general state the expectation value will not always be L/2. See for instance http://en.citizendium.org/wiki/Particle_in_a_box for a graphic demonstration.
PsiStar ( talk) 21:13, 2 March 2011 (UTC)
Dear Author, The formula for energy levels in higher dimensions seems to be wrong. For the two dimensional equation it states currently: E_nx,ny = h^2/2m (k_nx + k_ny)^2 = h^2/2m (n_x pi/L_x + n_y pi/L_y)^2. But it should read instead: E_nx,ny = h^2/2m (k_nx^2 + k_ny^2) = h^2/2m ((n_x pi/L_x)^2 + (n_y pi/L_y)^2). As the eigenvalues of the 2D-Laplacian are 2,5,5,8,10 ... = (1+1),(1+4),(4+1),(4+4),(1+9) ... The same applies to the three dimensional equation. Please verify and correct this. — Preceding unsigned comment added by Pia novice ( talk • contribs) 23:11, 22 February 2012 (UTC)
If the boundary conditions are changed from "x=0 to x=L" to "x=-L/2 & x=+L/2", how to find the two constants A & B. Since in this case none of the constants goes to zero. — Preceding unsigned comment added by Imrohit2611 ( talk • contribs) 09:12, 14 April 2018 (UTC)
The derivation in the article is largely centered around the time-dependent SE, yet a discussion of the discrete stationary states is mixed into the text, without any mention that those are solutions of the time-independent SE. The effect must be thoroughly confusing to anyone who doesn't firmly master Quantum Mechanics but has a serious interest in learning more about it (presumably our target audience).
I would suggest to dedicate an equal amount of space to the time-independent and time-dependent solutions, each under their respective subheadings.
I'm tempted to put a Cleanup template on top based on this issue alone (and there are more on this page).
OneAhead (
talk)
14:25, 8 April 2020 (UTC)
@ Luman2009: I'm not a physicist, so I apologize if I'm totally wrong here. Is the material in the new section "A more general analytically solvable problem in quantum mechanics" explicitly supported by the sources? As a layman, it seems to me like it might be original research, so I wanted to double-check. BalinKingOfMoria ( talk) 02:11, 22 August 2022 (UTC)
@
Luman2009: Discussion about
Kronig-Penney type of model does not belong to this article. This article is about an infinite potential well. If you make multiple copies of infinite potential wells, you do not get any band dispersion, as the electronic states in the wells are completely independent of each other. I have removed the content.
Jähmefyysikko (
talk)
11:37, 24 July 2023 (UTC)
The above text that has been striken out was based on the misunderstanding of the model. New try: So the model is an infinite potential well with additional priodic potential inside the well. I think it is too far removed from the original model to be discussed here. Jähmefyysikko ( talk) 11:41, 24 July 2023 (UTC)
The infinite potential well with Dirichlet boundary isn't a physical model, and furthermore fails to present a consistent quantum mechanical system, due to the bad domain of definition of with the chosen boundary conditions. Some sources:
https://link.springer.com/book/10.1007/978-1-4614-7116-5 Ch 9.6 "A Counterexample" (ominous),
https://courses.physics.illinois.edu/phys508/fa2017/amaster.pdf Section 4.2.4 (speedy overview), and
https://arxiv.org/abs/quant-ph/0103153 2 "The infinite potential well : paradoxes"
This last paper makes the following observation regarding the Hamiltonian operator and its square:
With state vector (on the interval), we have , and attempts to measure the squared energy yield either:
where are even energy eigenvalues, versus
. Disaster.
It all comes down to the spectral theory: The construction given with boundary conditions is a space where the momentum operator fails to be an essentially self-adjoint operator, after this everything falls apart. One can only resolve this by modifying the wave function space, with twisted periodic boundary conditions for some to be decided. The intuition that is wrong, and perhaps fails us here because the potential is infinite. A better intuition is that our wave functions should start in , and position eigenvectors may end up being continuous under constraint by the system.
Of course, this particular particle-in-a-box is still a useful model to study in the beginning, which creates a tension. But surely the fact that the derivation leads to contradictions, enforces bad intuitions, obscures the free variable and the physically relevant twisted boundary, and is fundamentally incompatible with the underlying theory should be signposted somewhere for readers. There seem to be a lot of misconceptions out there regarding these questions, and this is a fundamental example in the pedagogy. Jagmanjg ( talk) 09:36, 19 March 2024 (UTC)