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

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

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