Talk:Degenerate energy levels

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What is the significance of giving "two states have the same energy" a special name. The word pops up everywhere in physics. OK, so there are two states and if you are trying to analyze your system using energy, you can't tell. But if you perturb your system, you can get energy splitting, and detect that there were more states where you previously thought there was only one. It still seems like a non-interesting bit of information, like 3 and 5 are both prime, or that Francium and Caesium have the same density. Can someone pleas explain?

I realize that this is a rather old question, but in case someone else comes across this, here's a quickie. The energy levels of a system can be viewed as the eigenvalues of the time-independent Schrödinger equation, and when you have more than one eigenvector corresponding to a given eigenvalue, you say that it is a degenerate eigenvalue (or eigenenergy) (cf. Degeneracy_(mathematics)). Now, I haven't done the research to see which is the chicken and which is the egg in this case, but I'm pretty sure the term for degenerate eigenvalues came along before QM. Zak.estrada (talk) 20:01, 19 July 2011 (UTC)

"Degenerate" in both the physics and mathematics sense comes originally from the German "entartete". A Google Books search shows that this was used in mathematics journals in the 1880s, long before quantum mechanics. ServiceAT (talk) 00:57, 21 November 2011 (UTC)

Merge suggestion

Today, I came across separate article for degenerate energy level and degenerate orbital. The later is basically a specific case of the first. Both article are currently unreferenced and stubby. I think there is a serious chance of improvement if the two are merged, (and sources are added).TR 14:55, 17 August 2011 (UTC)

Degenerate states are much more general than degenerate orbitals. So, if anything, the latter article should be merged into this one as a section of it. ServiceAT (talk) 00:57, 21 November 2011 (UTC)

I went ahead and just redirected that article to this one. It didn't really have anything new to add. —METS501 (talk) 07:26, 26 November 2011 (UTC)

Error in Degeneracy and symmetry section

I think we should modify or reword the (unsourced) Proof that the existence of an operator which commutes with the Hamiltonian results in degeneracy. The last two lines are which means that $S|\alpha \rangle$ is also an energy eigenstate with the same eigenvalue E, i.e. the two states $|\alpha \rangle$ and $S|\alpha \rangle$ are degenerate. I agree that $S|\alpha \rangle$ is an energy eigenstate with the same eigenvalue, but I do not agree that $|\alpha \rangle$ and $S|\alpha \rangle$ are necessarily two different states. It is entirely possible that $S|\alpha \rangle$ is the same state as $|\alpha \rangle$, with or without a phase factor of (-1) in the wave function.

As one example among many, consider the Molecular orbital diagram of the water molecule. The lowest (2a₁) orbital is symmetric with respect to both the molecular plane and the plane which bisects the line joining the two hydrogen atoms. Either of these reflections is therefore a symmetry operator which commute with the Hamiltonian. However each reflection operator produces the same 2a₁ orbital which is not degenerate. Dirac66 (talk) 22:11, 25 October 2015 (UTC)

Further to the above, I have decided that the simplest fix is to add the words Provided that the new function is linearly independent of the initial function. to the last sentence. Also, I will delete the title Proof that ... results in degeneracy, since it fact it may result in degeneracy provided ....Dirac66 (talk) 23:20, 25 October 2015 (UTC)

Image to table

Per Wikipedia:Files for discussion/2016 September 10#File:Degrees of degeneracy of different levels for a particle in a square box.jpg, the table of degrees of degeneracy has been converted from an image to a wikitext table. Original author: Sarbajaya kundu (talk · contribs). This talk page comment serves as attribution. Deryck C. 17:02, 14 October 2016 (UTC)

Plagiarism tag unjustified

I believe that the plagiarism tag added by editor 73.210.155.96 claiming that "entire sections, section after section, that violate the WP plagiarism guideline" is not justified by the evidence and should be deleted. It is certainly true that much of this article is unreferenced, and it would be appropriate to add more tags requesting citations for specific statements or sections, or questioning whether some statements constitute original research. The evidence for these problems is apparent on reading the problematic sections of this article.

However plagiarism is a different matter, as it implies copying another source without attribution, or perhaps copying too closely with attribution. In order to show that a passage is plagiarized, it is necessary to find the alleged source and compare it with the allegedly plagiarized passage. If this were done, Wikipedia editors could remedy the specific problems. It is not sufficient to just imply that some unspecified passages may be plagiarized from some unspecified sources.

For what it is worth, my own (unproven) belief is that many of the problematic passages may be due to "unconscious plagiarism," meaning that editors have written what they "know" to be true because they read it (or even taught it) years ago, and have been too lazy to look for reliable sources. This would justify "citation needed" tags, but not plagiarism tags. Dirac66 (talk) 21:00, 21 January 2017 (UTC)

No comments after 3 weeks, so I will now remove this tag. Dirac66 (talk) 12:07, 10 February 2017 (UTC)

Wrong sentence

„ For an N-particle system in three dimensions, a single energy level may correspond to several different wave functions or energy states. These degenerate states at the same level are all equally probable of being filled“ is misleading at best and wrong at worst. What does it mean that they are all „equally likely to be filled“ ?? A priori there is not even a reason why the eigenspace corresponding to some eigenvalue of the Hamiltonian should be finite-dimensional, and if it is not, then there is no such thing as a uniform measure over the basis of the eigenspace. The correct statement can be found at postulate 6 here. The uniform measure is only the correct one if the modulus of the inner product of the normalized basis vectors of the eigenspace with the state that the system is in is always the same. —Maximilian Janisch (talk) 11:28, 31 October 2021 (UTC)