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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.
|Uncontrolled Keywords:||pseudo-Hermiticity, PT invariance, Moyal products, HERMITIAN QUANTUM-MECHANICS, SYMMETRY, BRACKETS, MODEL|
|Subjects:||Q Science > QC Physics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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