Eigenvalues and eigenfunctions of the anharmonic oscillator V(x,y)=x~2y~2

摘要

We obtain sufficiently accurate eigenvalues and eigenfunctions for the anharmonic oscillator with potential V(x,y)=x~2y~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.