Formal solutions of stargenvalue equations

Details Formal solutions of stargenvalue equations Formal solutions of stargenvalue equations

2001-10-05

arxiv.org/abs/quant-ph/0110035v2

Annals of Physics 311/1 (2004) 120-151

Physics

Quantum Physics

29 pages. Revised version, to appear in Annals of Physics

Scientific paper

10.1016/j.aop.2003.11.004

The formal solution of a general stargenvalue equation is presented, its properties studied and a geometrical interpretation given in terms of star-hypersurfaces in quantum phase space. Our approach deals with discrete and continuous spectra in a unified fashion and includes a systematic treatment of non-diagonal stargenfunctions. The formalism is used to obtain a complete formal solution of Wigner quantum mechanics in the Heisenberg picture and to write a general formula for the stargenfunctions of Hamiltonians quadratic in the phase space variables in arbitrary dimension. A variety of systems is then used to illustrate the former results.

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