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The Wentzel-Kramers-Brillouin approximation method applied to the Wigner function.
- Source :
-
Journal of Mathematical Physics . 2016, Vol. 57 Issue 6, p1-13. 23p. 12 Graphs. - Publication Year :
- 2016
-
Abstract
- An adaptation of the Wentzel-Kramers-Brilluoin method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between the phase σ(r) of a wave function expi(i/Ƌσ(r)) and its respective Wigner function is derived. Formulas to calculate the Wigner function of a product and of a superposition of wave functions are proposed. Properties of a Wigner function of interfering states are also investigated. Examples of this quasi-classical approximation in deformation quantization are analysed. A strict form of the Wigner function for states represented by tempered generalised functions has been derived. Wigner functions of unbound states in the Poeschl-Teller potential have been found. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 57
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 116598787
- Full Text :
- https://doi.org/10.1063/1.4954071