A note on a class of exact solutions for a doubly anharmonic oscillator

Abstract

We examine a class of exact solutions for the eigenvalues and eigenfunctions of a doubly anharmonic oscillator defined by the potential $V(x)={\omega }^2/2x^2+\lambda x^4/4+\eta x^6/6$, $\eta >0$. These solutions hold provided certain constraints on the coupling parameters ${\omega }^2$, $\lambda$ and $\eta$ are satisfied.

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