  An adaptation of the WKB 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 $\sigma(\vec{r})$ of a wave function $\exp
\left(\frac{i}{\hbar} \sigma(\vec{r}) \right)$ 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.
