The Wentzel-Kramers-Brillouin approximation method applied to the Wigner function

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Abstract

© 2016 Author(s). 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 (i/h σ(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.
Original languageAmerican English
JournalJournal of Mathematical Physics
DOIs
StatePublished - 1 Jun 2016

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