S'Darboux coordinates and WKB approximations in deformation quantization

Details S'Darboux coordinates and WKB approximations in deformation quantization S'Darboux coordinates and WKB approximations in deformation quantization

2005-06-29

arxiv.org/abs/math-ph/0506074v1

Physics

Mathematical Physics

14 pages, no figures

Scientific paper

We introduce a method for calculating the joint spectra of functions which comprise a quantum integrable system under a deformation quantization star product. The main result involves a construction by formal power series in h-bar of s'Darboux coordinates, a concept we introduce for the star product analogue of Darboux normal coordinates. We will find that underlying the quantum integrable system is a set of s'Darboux coordinates which in turn gives rise to number operators for the system. We present an explicit correction to the lowest order Bohr-Sommerfeld or EBK quantization rule.

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