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 Mathematics, Computer Science & Engineering > Mathematics
URI:	http://openaccess.city.ac.uk/id/eprint/697

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