Talk:Perturbation theory (quantum mechanics)

message: I will correct it, but I didn't use wiki formulas, so I apologize if output is not perfect.  —Preceding unsigned comment added by 131.180.87.254 (talk) 13:05, 22 September 2008 (UTC)
thread_title:  Degenerate theory have false statement that first order correction in energy is the same 

message: The article claims:
The first-order equation is
: H_0 |n^{(1)}\rang + V |n^{(0)}\rang = E_n^{(0)} |n^{(1)}\rang + E_n^{(1)} |n^{(0)}\rang 
Multiply through by <n(0)|.  The first term on the left-hand side cancels with the first term on the right-hand side. (Recall, the unperturbed Hamiltonian is hermitian). This leads to the first-order energy shift:
(emphasis added)
After multiplying through by <n(0)|, it looks like the first term on the left-hand side goes to zero on it's own (H_0 pops out of the bra-ket and turns into an E_0, leaving you with <n(0)| n(1)> which is zero (orthogonality). (As opposed to canceling with the term on the right-hand side.) I believe the statement I've italicized is incorrect.--GameGod (talk) 18:22, 7 December 2007 (UTC)
replies: text: * Who said that <n(0)| n(1)> is zero? The <n(0)> and <n(1)> don't belong to the same base (as opposed to, for example <n(0)> and <n+1(0)>) Gglanzani (talk) 16:44, 29 January 2010 (UTC)
thread_title:  Cancellation of Terms 

message: Could someone highlight Nonperturbative and explain it more explicity ... the wlnk comes here ... but then it's not highlighted nor explained well ... thanks. J. D. Redding 16:24, 10 March 2006 (UTC)
thread_title:  Nonperturbative?

message: I have modified the rating of this article and linked it to mathematical project. It contains a lot of relevant material that is essential in the understanding of quantum mechanics and, mostly, of quantum field theory where perturbation theory is an essential tool.
Pra1998 (talk) 08:26, 3 December 2008 (UTC)
thread_title: Rating and Mathematics

message: I really think this article needs at least one example of perturbation theory at work.  A quantum well in a weak electric field (the quantum-confined Stark effect) is about as simple as this gets.  This also gives us the opportunity to discuss the limitations of the approximation: "new" behaviour caused by the electric field, such as Fang-Howard tunnelling is not accounted for by perturbation theory.  Also, we can look at the range of perturbing electric field for which the model is valid: when the matrix element of the perturbing potential becomes comparable to the separation between the unperturbed states, the second-order perturbation terms fail to converge.
Does anyone else think such a section would be useful?  If so, I'll start writing it! Papa November (talk) 09:30, 27 August 2009 (UTC)
thread_title:  Examples 

message: Hiya,
for a project I needed perturbation theory to third order in the states. I could not find anything going above second order in the states in any of the common QM textbooks I looked at. So I decided to re-derive it myself, and while of course I cannot be absolutely sure *my* result is correct, it does agree with the numerical solution I got, whereas the wikipedia version has a significant deviation from numerical & my perturbative solution. Therefore I strongly suspect the expression for third order of states, and possibly fourth order and higher in energy and states, to be wrong. I could exchange the third order in states with the version I have, but in any case I think it would be good to remove the wrong statements.
S.John
217.93.234.75 (talk) 17:49, 6 July 2010 (UTC)
replies: text:  I have restored the higher order corrections. Regarding the third order energy correction, I can not see any difference with "your" correct results. I don't know if the higher order formulas are right or not, but what I believe is if you can not prove that they are wrong, you should not simply delete them. If you do think there is a mistake, you should show it here, and correct it in the article.Everett (talk) 01:44, 17 February 2011 (UTC)
thread_title:  Third- and possibly higher-order expressions are wrong 

message: Please, please: WP:MOS and WP:MOSMATH both exist.
: 
I found
* "Hellman–Feynman" appearing repeatedly with a hyphen rather than an en-dash;
* -1 instead of −1;
* Indiscriminate italicizing of everything in non-TeX math notation including even parentheses and digits;
* Numerous cases of initial letters capitalized merely because they were in section headings.
* Instances of </math>. or </math>, instead of .</math> or ,</math>.  The punctuation often fails to get properly aligned when it's outside of the "math" tags;
* Failures to indent "displayed" things in math tags (via a preceding colon);
* etc., etc., .....  See my recent edit.
I've cleaned up a lot of this. Michael Hardy (talk) 23:09, 18 October 2012 (UTC)
thread_title:  spelling, etc. 

message: In the article it says:
"Since the overall phase is not determined in quantum mechanics, without loss of generality, we may assume \lang n^{(0)}|n \rang  is purely real." 
I'm not sure but this seems to be simply wrong. Of course you can choose your _overall_ phase at will in QM, because it will cancel out whenever calculating an expectation value. Therefore one cannot simply "make" or "assume" something like \lang n^{(0)}|n \rang  to be real, a phase factor would have to be multiplied to both sides and would not change the result at all...
92.195.40.81 (talk) 12:51, 20 January 2013 (UTC)
thread_title:  Error in assumption 

message: I think that it is started and edit war on the section about "strong perturbation theory". The same anonymous from Boston (MA) deleted all of it twice. Maybe some Administrator can act to stop this? Thanks.--Pra1998 (talk) 19:47, 4 March 2014 (UTC)
replies: text: He has switched IP, and is now 18.62.31.139, also from MIT, and I left a warning on that IP's Talk page. Any further peremptory editing without discussion on this page by him or his IP covers first should  be treated as plain vandalism. Cuzkatzimhut (talk) 21:13, 10 December 2014 (UTC)
replies: text: Fine. Thanks a lot.--Pra1998 (talk) 23:10, 10 December 2014 (UTC)
thread_title:  Edit war 

message: I'm very sorry for some mistakes in the page Perturbation theory but I think the original purpose is rather correct: I wish to specify that these ones are applications of analytical perturbation methods to QM, while many other fields have seen perturbation methods like neutronics basing on linear Boltzmann equation, viscoelasticity and so on. That is also the reason I have just suggested in the discussion of [Mathematical] Perturbation Theory page to solve the ambiguity on one hand by inverting the redirect with perturbation methods, and on the other hand to rename the Perturbation Theory (QM) page into Quantum perturbation Theories, (since there are more than one QPT).95.238.49.157 (talk) 18:14, 7 October 2014 (UTC)
replies: text: As indicated on my talk page plea, I have no interest in said wildcat relabelling stunts, but the loss of the explanatory sentence "The idea is to start with a simple system for which a mathematical solution is known, and add an additional perturbing Hamiltonian representing a weak disturbance to the system." from the introduction is manifestly regrettable. Cuzkatzimhut (talk) 13:17, 8 October 2014 (UTC)
thread_title:  Rename the article into Quantum Perturbation Theories 

message: From the article: "the calculation of the electron's magnetic moment has been found to agree with experiment to eleven decimal places."
http://www.oberlin.edu/physics/dstyer/StrangeQM/Moment.pdf
Is a viewable discussion of the context with it's citation to the data being  Physical Review D 85 (2012) 033007
I'm much out of my depth in both this topic and in Wikipedia editing however, so I will leave any changes to the good people with higher capabilities. 98.230.96.47 (talk) 19:31, 5 April 2015 (UTC)
replies: text: Though I'm only a moderately good person and have few capabilities, I did add the Phys. Rev. D paper. The other pdf, while a good read and undoubtedly reliable, does not pass as a reference unfortunately. Next time, add it yourself! YohanN7 (talk) 22:59, 5 April 2015 (UTC)
thread_title:  Source for experimental and theoretical value precision 

message: Can quantum correction please be made to point to this article? 96.40.48.159 (talk) 18:17, 14 October 2019 (UTC)
replies: text: Bad idea. A quantum correction is a correction of $O(\hbar)$ to a classical expression, and not a small coupling correction to a quantum expression as detailed here. Why on earth would one imagine this could be otherwise? Cuzkatzimhut (talk) 21:15, 14 October 2019 (UTC)
replies: text: Ok, guess I should apologize for not being an expert, asshole?  Where should quantum correction redirect, then?  I see it used all the time here, but there's not a proper redirect. 96.40.48.159 (talk) 22:37, 14 October 2019 (UTC)
thread_title:  Quantum correction 

message: First order:
"Since the overall phase is not determined in quantum mechanics, without loss of generality, in time independent theory we may assume {\displaystyle \langle n^{(0)}|n^{(1)}\rangle }{\displaystyle \langle n^{(0)}|n^{(1)}\rangle } is purely real. Therefore,
{\displaystyle \left\langle n^{(0)}\right|\left.n^{(1)}\right\rangle =\left\langle n^{(1)}\right|\left.n^{(0)}\right\rangle ,}"
There is a minus sign missing.
Don't want to edit the article myself, because someone will again demand a citation for basic math.
Edit: Well I don't know how to Wikipedia, so excuse me for the botched formula
:Please sign your comments! Further, read all three formulas involved, and make a minimal effort to understand the logic flow of what is being asserted: It is because both the sum and difference of two numbers vanish that both numbers vanish. Cuzkatzimhut (talk) 16:49, 9 April 2020 (UTC)
replies: text: I get it now. It read like a=a* implies a=0, since it said "therefore a=a* leads to a=0" where 'a' is the term in question. But well... 129.69.48.35 (talk) 13:50, 10 April 2020 (UTC)
thread_title:  Correction to "Time-independent perturbation theory" 

message: I have implemented the Energy corrections with some minimal example. After spending many ours I came to the suspicion that the 5th oder energy correction might contain some error. Can someone check that? 185.58.28.55 (talk) 21:48, 4 December 2022 (UTC)
thread_title:  5th oder Energy correction, time indepandent 

message: Can someone post what this looks like? I.e. Vnk is the same for all k in the degenerate space, so the expression for first order correction of eigenvectors goes to infinity. Iuvalclejan (talk) 23:27, 10 September 2023 (UTC)
thread_title:  eigenvector perturbation to first order, when degenerate energy NOT lifted to first order