Pseudo-Hermitian version of the charged harmonic oscillator and its "forgotten" exact solutions
arXiv:quant-ph/0206085
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.
17 pages incl. 2 tables