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

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

2002-06-13

arxiv.org/abs/quant-ph/0206085v1

Physics

Quantum Physics

17 pages incl. 2 tables

Scientific paper

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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