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 the position-dependent effective mass Schrödinger equation for two cases belonging to the generalized Laguerre polynomials. Using a suitable quantum canonical transformation, expectation values of position and momentum operators are obtained analytically in order to verify the universality of Heisenberg’s uncertainty principle.