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

Mehmet Sezgin

doi:10.3390/universe6030038

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.

Highlights

Since Lie groups have both group and manifold structures, they are widely used in various branches of mathematics and physics
Hamiltonian of the physical system is related to the Casimir operator of the group by [C − q] = Q[H − E], where C
In the group theory approach, an algebraic solution of the Schrödinger equation is obtained from the symmetry property of the physical system

Summary

Introduction

Since Lie groups have both group and manifold structures, they are widely used in various branches of mathematics and physics. Hamiltonian with position-dependent mass related to the Casimir operator of the Lie group. The Casimir operator of the group SL(2,R) is associated with the Hamiltonian of the physical system as The infinitesimal operators Jk corresponding to one parameter subgroups ωk of the regular d representation of the group is given by Jk = −i dτ

Results

Conclusion