Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation

We introduce a generalization of the Dunkl-derivative with two parameters to study the Schrödinger equation in Cartesian and polar coordinates in two dimensions. The eigenfunctions and the energy spectrum for the harmonic oscillator and the Coulomb problem are derived in an analytical way and it is shown that our results are properly reduced to those previously reported for the Dunkl derivative with a single parameter.