Czechoslovak Journal of Physics

, Volume 56, Issue 9, pp 899–908 | Cite as

Isospectral Hamiltonians from Moyal products

  • C. Figueira de Morisson Faria
  • A. Fring
Article

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 −x4-potential and the ubiquitous harmonic oscillator in a complex cubic potential.

Key words

pseudo-Hermiticity PT invariance Moyal products 

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Copyright information

© Institute of Physics, Academy of Sciences of Czech Republic 2006

Authors and Affiliations

  • C. Figueira de Morisson Faria
    • 1
  • A. Fring
    • 1
  1. 1.Centre for Mathematical ScienceCity UniversityLondonUK

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