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

TL;DR

This paper explores exact solutions for the eigenvalues and eigenfunctions of a doubly anharmonic oscillator with a specific potential, under certain parameter constraints, contributing to quantum mechanics solution methods.

Contribution

It introduces a class of exact solutions for a complex anharmonic oscillator potential, expanding analytical methods in quantum mechanics.

Findings

Derived explicit eigenvalues and eigenfunctions

Identified parameter constraints for exact solutions

Enhanced understanding of anharmonic oscillator spectra

Abstract

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