[coupled harmonic oscillators] old thread- need elaboration

Click For Summary

Discussion Overview

The discussion revolves around the challenge of uncoupling the Hamiltonian for coupled harmonic oscillators. Participants are seeking clarification and assistance in resolving the issue of residual terms in their calculations.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant requests an explanation regarding the uncoupling of the Hamiltonian for coupled harmonic oscillators.
  • Another participant suggests using a rotation transformation to facilitate the uncoupling process, proposing specific equations for the transformation.
  • A participant indicates that despite attempting the suggested rotation, they still encounter a mixed term (xy) in their results.
  • Another participant encourages showing the work done to identify potential errors in the calculations.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing different experiences and challenges related to the uncoupling process, and no consensus on the effectiveness of the proposed methods.

Contextual Notes

Participants have not fully detailed their assumptions or the specific context of their calculations, which may impact the discussion.

rsaad
Messages
76
Reaction score
0
Physics news on Phys.org


Did you try the proposed rotation?

##x'=\cos(\alpha)x + \sin(\alpha)y##, ##y'=-\sin(\alpha)x + \cos(\alpha)y##

Where α has to be determined to uncouple the Hamiltonian.
 


Yes i tried but I am still getting xy term
 
You could show your work here, this would help to find the error.
 

Similar threads

  • · Replies 14 ·
Replies
14
Views
4K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
13
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 0 ·
Replies
0
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K