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

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

Publishing date

2005-12-07

URL

arxiv.org/abs/quant-ph/0512055v2

Journals

Phys. Lett B 634 (2006) 84

Science

Physics

Field

Quantum Physics

Additional info

References added

Type

Scientific paper

Digital Object Identifier

10.1016/j.physletb.2006.01.022

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.

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