Eigenvalues and eigenfunctions of the anharmonic oscillator $V(x,y)=x^{2}y^{2}$

Abstract

We obtain sufficiently accurate eigenvalues and eigenfunctions for the anharmonic oscillator with potential $V(x,y)=x^{2}y^{2}$ by means of three different methods. Our results strongly suggest that the spectrum of this oscillator is discrete in agreement with early rigorous mathematical proofs and against a recent statement that cast doubts about it.