Physical Review A

Wigner function of Morse potential eigenstates

Alejandro Frank, Ana Leonor Rivera, Kurt Bernardo Wolf

Published Apr 13, 2000• 54 citations

Abstract

We find the analytic expressions and obtain plots of the Wigner distribution function for the bound eigenstates of the Morse potential on quantum phase space.Received 17 August 1999DOI:https://doi.org/10.1103/PhysRevA.61.054102©2000 American Physical Society

DOI: 10.1103/physreva.61.054102

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Physical Review A

Wigner function of Morse potential eigenstates

Alejandro Frank, Ana Leonor Rivera, Kurt Bernardo Wolf

Published Apr 13, 2000• 54 citations

Publisher

Abstract

DOI: 10.1103/physreva.61.054102

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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.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.

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Physica ScriptaJan 1, 199323 citations

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.