Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry
Abstract
It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for certain shape-invariant potentials, including a non-hermitian version of the standard Jaynes-Cummings model for which the parent supersymmetric Hamiltonian is the superoscillator. The positive-definite metric operator in the Hilbert space is constructed explicitly along with the introduction of a new inner product structure, so that the eigenstates form a complete set of orthonormal vectors and the time-evolution is unitary.
Keywords
Cite
@article{arxiv.quant-ph/0501087,
title = {Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry},
author = {Pijush K. Ghosh},
journal= {arXiv preprint arXiv:quant-ph/0501087},
year = {2009}
}
Comments
10 pages (v1); 18 pages, expanded version with several new results (v2); minor cosmetic changes, to appear in J. Phys. A: Math. & Gen