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

[cks]

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?

 

[HallsofIvy]

"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.