An anharmonic oscillator with the potential V(x,y) = 1/2(mw²x²) + 2mw²y² , How am I supposed to solve this to get position eigenfunctions and energy eigenvalues ?

Can you use separation of variables method?

How am I supposed to use ladder operators in solving them likewise, as in separating the variables ? Also how am I supposed to calculate energy eigenvalues as well ?

How am I supposed to use ladder operators in solving them likewise, as in separating the variables ? Also how am I supposed to calculate energy eigenvalues as well ?

 

 

Have a look at Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis, D. Lenis, Symmetry Algebra of the Planar Anisotropic Quantum Harmonic Oscillator with Rational Ratio of Frequencies, arXiv:hep-th/9402099v1

 

They study the problem for rational ratio of frequencies. I know that specific ratios have also been studied. I wonder if the general case is just not integrable? Let us know what you find out, I am generally interested.