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Isospectral Hamiltonians from Moyal products

Faria, C. F. D. M. & Fring, A. (2006). Isospectral Hamiltonians from Moyal products. Czechoslovak Journal of Physics, 56(9), pp. 899-908. doi: 10.1007/s10582-006-0386-x

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.

Publication Type: Article
Publisher Keywords: pseudo-Hermiticity, PT invariance, Moyal products, HERMITIAN QUANTUM-MECHANICS, SYMMETRY, BRACKETS, MODEL
Subjects: Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
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