Moyal products -- a new perspective on quasi-hermitian quantum mechanics

Details Moyal products -- a new perspective on quasi-hermitian quantum mechanics Moyal products -- a new perspective on quasi-hermitian quantum mechanics

2006-02-22

arxiv.org/abs/quant-ph/0602187v1

Physics

Quantum Physics

14 pages. Submitted to J Phys A special issue on The Physics of Non-Hermitian Operators

Scientific paper

10.1088/0305-4470/39/32/S19

The rationale for introducing non-hermitian Hamiltonians and other observables is reviewed and open issues identified. We present a new approach based on Moyal products to compute the metric for quasi-hermitian systems. This approach is not only an efficient method of computation, but also suggests a new perspective on quasi-hermitian quantum mechanics which invites further exploration. In particular, we present some first results which link the Berry connection and curvature to non-perturbative properties and the metric.

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