2005/01/31 by Pijush K. Ghosh
Physics and Astronomy · #quant-ph #hep-th
paper · pdf · doi:10.1088/0305-4470/38/33/007
published as J.Phys. A38 (2005) 7313-7324 · 10 pages (v1); 18 pages, expanded version with several new results (v2); minor cosmetic changes, to appear in J. Phys. A: Math. & Gen
arxiv created 2005/07/14 · arxiv updated 2009/12/01
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.