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Eigenvalues and eigenfunctions of the anharmonic oscillator $V(x,y)=x^{2}y^{2}$
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quant-phmath-phmath.MP
keywords
oscillatoranharmoniceigenfunctionseigenvaluesaccurateagreementcastdifferent
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.
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