Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics

F G Scholtz; H B Geyer

doi:10.1016/j.physletb.2006.01.022

Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics

Quantum Physics 2009-11-11 v2

Authors: F G Scholtz , H B Geyer

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

The Moyal product is used to cast the equation for the metric of a non-hermitian Hamiltonian in the form of a differential equation. For Hamiltonians of the form $p^2+V(ix)$ with $V$ polynomial this is an exact equation. Solving this equation in perturbation theory recovers known results. Explicit criteria for the hermiticity and positive definiteness of the metric are formulated on the functional level.

Keywords

moyal product quasi-hermitian quantum mechanics metric non-hermitian hamiltonian perturbation theory

Cite

@article{arxiv.quant-ph/0512055,
  title  = {Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics},
  author = {F G Scholtz and H B Geyer},
  journal= {arXiv preprint arXiv:quant-ph/0512055},
  year   = {2009}
}

Comments

References added

Related papers

View all related →