Perturbation of 2D Oscillator along one axis

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SUMMARY

The discussion focuses on the perturbation of a two-dimensional harmonic oscillator, specifically addressing the perturbation defined as H' = -qfy. Participants highlight that all elements of the matrix H' appear to be zero, complicating the construction of a diagonal matrix in the subspace. However, it is noted that there are nonzero diagonal elements of H' when considering quantum states n=0 and n=1. This indicates that further exploration of these states is essential for resolving the matrix construction issue.

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The problem given is a perturbation on the two dimensional harmonic oscillator where the perturbation is simply: H'=-qfy.

It seems that all of the elements of the matrix H' are zero and so constructing a diagonal matrix in the subspace is eluding me. Any ideas?
 
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There are nonzero diagonal elements of H'
try n=0 and n=1
 

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