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Pseudo-Hermitian version of the charged harmonic oscillator and its "forgotten" exact solutions

Miloslav Znojil
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Abstract

An unusual type of the exact solvability is reported. It is exemplified by the Coulomb plus harmonic oscillator in D dimensions after a complexification of its Hamiltonian which keeps the energies real. Infinitely many bound states are found in closed form which generalizes the even-parity harmonic-oscillator states at zero charge. Apparently, the model is halfway between exact and quasi-exact.

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Miloslav Znojil. 2002-06-13. Pseudo-Hermitian version of the charged harmonic oscillator and its "forgotten" exact solutions. https://arxiv.org/abs/quant-ph/0206085

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