Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  Diagram-like perturbation theory in quantum mechanics

+ 3 like - 0 dislike
2111 views

There seems to be a formalism of quantum mechanics perturbation that involve something like Feynman diagrams. The advantage is that contrary to the complicated formulas in standard texts, this formalism is intuitive and takes almost zero effort to remember (to arbitrary orders).

For example, consider a two level atom $\{|g\rangle, |e\rangle\}$ coupled to an external ac electric field of frequency $\omega$. Denote the perturbation by $\hat V$, with nonzero matrix element $\langle e|\hat V |g\rangle$.

Then the second order energy correction reads $$E^{(2)} = \langle e|\hat V |g\rangle\frac{1}{\omega_g - \omega_e +\omega} \langle g|\hat V |e\rangle + \langle e|\hat V |g\rangle\frac{1}{\omega_g - \omega_e -\omega} \langle g|\hat V |e\rangle $$ where the first term corresponds to the process absorb a photon then emit a photon while the second process is emit a photon then absorb a photon.

Does anybody know the name of this formalism? And why it is equivalent to the formalism found in standard texts?

This post imported from StackExchange Physics at 2014-03-22 16:58 (UCT), posted by SE-user ChenChao
asked Oct 27, 2012 in Theoretical Physics by ChenChao (35 points) [ no revision ]

2 Answers

+ 2 like - 0 dislike

There is an exposition of a diagrammatic representation of the terms in the quantum mechanical perturbation expansion here. Basically the diagrams are just used to represent the combinatorial properties resulting from eigenstate degeneracy.

(Just for fun there is also a diagrammatic approach to perturbation expansions in classical mechanics here).

This post imported from StackExchange Physics at 2014-03-22 16:59 (UCT), posted by SE-user twistor59
answered Oct 27, 2012 by twistor59 (2,500 points) [ no revision ]
Thank you! But the first reference is sophisticated and too mathematical. The formalism I'm looking for is quite intuitive and physical.

This post imported from StackExchange Physics at 2014-03-22 16:59 (UCT), posted by SE-user ChenChao
+ 1 like - 0 dislike

Try Shankar Intro to Quantum Mechanincs page 489, he discusses the mathematical connection and the relation to feynman diagrams, or rather all the possible paths of interaction:

enter image description here

If you find something better, I'd be curious to know too.

This post imported from StackExchange Physics at 2014-03-22 16:59 (UCT), posted by SE-user AimForClarity
answered Sep 15, 2013 by AimForClarity (10 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\varnothing$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...