XXXV Workshop on Geometric Methods in Physics 26.06-2.07.2016
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# Jaromir Tosiek

## An adaptation of the WKB approximation to deformation quantisation

An adaptation of the WKB method in the deformation quantisation 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 $\sigma(\vec{r})$ of a wave function $\exp \left(\frac{i}{\hbar} \sigma(\vec{r}) \right)$ and its respective Wigner function is discussed. 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 investigated. Examples of the semiclassical approximation in deformation quantisation are analysed.