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.