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.