On the Solution of the Schrödinger Equation with Position-Dependent Mass

Abstract

We have considered the Iwasawa and Gauss decompositions for the Lie group SL(2,R). According to these decompositions, the Casimir operators of the group and the Hamiltonians with position-dependent mass were expressed. Then, the unbound state solutions of the Schrödinger equations with position-dependent mass were given.

Keywords

• lie group
• casimir operator
• schrödinger equation
• decomposition