Moyal equation—Wigner distribution functions for anharmonic oscillators

We investigate the structure of Wigner distribution functions of energy eigenstates of quartic and sextic anharmonic oscillators. The corresponding Moyal equations are shown to be solvable, revealing new properties of Schrödinger eigenfunctions of these oscillators. In particular, they provide alter...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-10, Vol.62 (10)
Main Author: Truong, T. T.
Format: Article
Language:English
Subjects:
Anharmonicity
Differential equations
Distribution functions
Eigenvectors
Energy distribution
Harmonic functions
Mathematical Physics
Oscillators
Physics
Wigner distribution
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Summary:We investigate the structure of Wigner distribution functions of energy eigenstates of quartic and sextic anharmonic oscillators. The corresponding Moyal equations are shown to be solvable, revealing new properties of Schrödinger eigenfunctions of these oscillators. In particular, they provide alternative approaches to their determination and corresponding eigenenergies, away from the conventional differential equation method, which usually relies on the not so widely known bi- and tri-confluent Heun functions.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0021132