What Does Isotropy Mean in a Two-Dimensional Harmonic Oscillator?

AI Thread Summary
The discussion centers on understanding the term "isotropic" in the context of a two-dimensional harmonic oscillator. Isotropic means that the system behaves identically in all directions, indicating that the spring constant is uniform in both dimensions. Participants clarify that isotropic does not imply "not changing," but rather uniformity in characteristics. The concept is often assumed in harmonic oscillator problems, allowing for simplifications in analysis. Overall, grasping the isotropic nature helps in solving for eigenfunctions and eigenvalues effectively.
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Find the find the eigenfunctions and eigenvalues of a two-dimensional isotropic harmonic oscillator.

I don't understand what does isotropic here mean.

isotropic can be defined "not changing" when the coordinate change to any other position. Am I correct?

Like mass, pressure, magnitude...

but how to imagine a two-dimensional isotropi harmonic oscillator? IF you were me, how would you imagine it?
 
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"isotropic" does not mean "not changing". It means "identical in all directions". Here it just means that the "spring constant" is the same in both directions. You can just ignore it- most harmonic oscillator problems assume "isotropic" without saying it.
 

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