We obtain the quantized momentum eigenvalues, Pn, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved deformed exponential-type potential which is constructed by temporal counterpart of the spatial form of these potentials. We also plot the variations of the improved deformed exponential-type potential with its momentum eigenvalues for few quantized states against the screening parameter.

arXiv:2007.14789Journal of Applied Mathematics and PhysicsJan 1, 20207 citations

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Physically Acceptable Solutions of an Eigenvalue Equation in Deformation Quantization

Jaromir Tosiek

Published Sep 28, 2012• 0 citations

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DOI: 10.1007/978-3-0348-0448-6_10

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\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.