Formal solutions of stargenvalue equations
Abstract
The formal solution of a general stargenvalue equation is presented, its properties studied and a geometrical interpretation given in terms of starhypersurfaces in quantum phase space. Our approach deals with discrete and continuous spectra in a unified fashion and includes a systematic treatment of nondiagonal 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.
 Publication:

Annals of Physics
 Pub Date:
 May 2004
 DOI:
 10.1016/j.aop.2003.11.004
 arXiv:
 arXiv:quantph/0110035
 Bibcode:
 2004AnPhy.311..120D
 Keywords:

 03.65.Ca;
 03.65.Db;
 03.65.Ge;
 Formalism;
 Functional analytical methods;
 Solutions of wave equations: bound states;
 Quantum Physics
 EPrint:
 29 pages. Revised version, to appear in Annals of Physics