Isospectral Hamiltonians from Moyal products

Abstract

Recently Scholtz and Geyer proposed a very efficient method to compute metric operators for non-Hermitian Hamiltonians from Moyal products. We develop these ideas further and suggest to use a more symmetrical definition for the Moyal products, because they lead to simpler differential equations. In addition, we demonstrate how to use this approach to determine the Hermitian counterpart for a Pseudo-Hermitian Hamiltonian. We illustrate our suggestions with the explicitly solvable example of the -x^4-potential and the ubiquitous harmonic oscillator in a complex cubic potential.

10 pages, to appear special issue Czech. J. Phys

References in corpus (4)

• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
• Time evolution of non-Hermitian Hamiltonian systems
• Moyal products -- a new perspective on quasi-hermitian quantum mechanics
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation

Cited by in corpus (7)

• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Non-Hermitian Hamiltonians of Lie algebraic type
• Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem
• Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
• Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
• Quasi-hermitian Quantum Mechanics in Phase Space