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Isospectral Hamiltonians from Moyal products

Authors
Publisher
Springer
Publication Date
Keywords
  • Qc Physics
Disciplines
  • Mathematics

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.

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