Abstract
we propose an easy-to-implement method for the calculation of eigenfunctions of polynomially perturbed higher-order quantum harmonic oscillators. Our method is based upon using the eigensolutions of the unperturbed harmonic oscillator as auxiliary gauging functions. The obtained eigenfunctions of perturbed harmonic oscillators can be used as a complete set of functions for analyzing related boundary value problems. Alternatively, the eigenfunctions can be utilized as the starting point for the calculation of even-order polynomial perturbations.
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