Generalized Laguerre Polynomials with Position-Dependent Effective Mass Visualized via Wigner's Distribution Functions

We construct, analytically and numerically, the Wigner distribution functions for the exact solutions of position-dependent effective mass Schr"odinger equation for two cases belonging to the generalized Laguerre polynomials. Using a suitable quantum canonical transformation, expectation values of position and momentum operators can be obtained analytically in order to verify the universality of the Heisenberg’s uncertainty principle.