Eigenvalue equation for a 1--D Hamilton function in deformation quantization
Mathematical Physics
2012-05-25 v2 math.MP
Quantum Physics
Abstract
The eigenvalue equation has been found for a Hamilton function in a form independent of the choice of a potential. This paper proposes a modified Fedosov construction on a flat symplectic manifold. Necessary and sufficient conditions for solutions of an eigenvalue equation to be Wigner functions of pure states are presented. The 1--D harmonic oscillator eigenvalue equation in the coordinates time and energy is solved. A perturbation theory based on the variables time and energy is elaborated.
Cite
@article{arxiv.1106.1358,
title = {Eigenvalue equation for a 1--D Hamilton function in deformation quantization},
author = {Jaromir Tosiek},
journal= {arXiv preprint arXiv:1106.1358},
year = {2012}
}
Comments
17 pages, 3 figures