Generation of exactly solvable non-Hermitian potentials with real energies

Abstract

A series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number of non-trivial partner potentials, defined over the whole real line, whose spectra are nearly exactly identical to the original potential.

10 pages, 2 figures, Based on the talk presented at the 1st International Workshop "Psedo-Hermitian Hamiltonians in Quantum Physics", held in Prague, June 16, 17, 2003. To be published in Czech. J. Phys. (Jan. 2004)