Formal solutions of stargenvalue equations
arXiv:quant-ph/0110035 · doi:10.1016/j.aop.2003.11.004
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.
29 pages. Revised version, to appear in Annals of Physics
References in corpus (5)
Cited by in corpus (14)
- Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
- Admissible states in quantum phase space
- Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit
- Wigner Measures in Noncommutative Quantum Mechanics
- Exact master equation for a noncommutative Brownian particle
- Features of Moyal Trajectories
- Coherent States Expectation Values as Semiclassical Trajectories
- Deformation Quantization and Wigner Functions
- Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces
- Metaplectic formulation of the Wigner transform and applications
- A symplectic extension map and a new Shubin class of pseudo-differential operators
- Shape invariance in phase space
- States in the Hilbert space formulation and the phase space formulation of quantum mechanics
- Stargenfunctions, generally parametrized systems and a causal formulation of phase space quantum mechanics