Formal solutions of stargenvalue equations
Quantum Physics
2009-11-07 v2
Abstract
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.
Cite
@article{arxiv.quant-ph/0110035,
title = {Formal solutions of stargenvalue equations},
author = {Nuno Costa Dias and Joao Nuno Prata},
journal= {arXiv preprint arXiv:quant-ph/0110035},
year = {2009}
}
Comments
29 pages. Revised version, to appear in Annals of Physics