Exact solutions of the Schrödinger equation with position dependent mass for the solvable potentials

In this work the infinitesimal operators of the regular representations of the group SL(R, 2) are considered. According to these infinitesimal operators the Casimir operator is expressed. The Hamiltonian H is related to Casimir operator C of the group. The energy eigenvalues and the corresponding eigenfunctions are given for the solvable potentials.