Year: 2010
Type: preprint
Abstract: We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied to potentials that are polynomial in an exponential. A Mellin transform converts the $\ast$-eigenvalue equations to difference equations, and factorized solutions are found directly for all values of the parameters. The symbols of both diagonal and off-diagonal density operator elements in the energy basis are found this way. The Wigner transforms of the density matrices built from the known wave functions are then shown to confirm the solutions.
Source: arXiv (Cornell University)
Authors: Belchev, B., Walton, M. A.
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1779518643