Relationship Between Integro-Differential Schrodinger Equation with a Symmetric Kernel and Position-Dependent Effective Mass

The solution of integro-differential Schrodinger equation (IDSE) which was introduced by physicists has a great role in the fields of science. The purpose of this paper comes in two parts. First, studying the relationship between integro-differential Schrodinger equation with a symmetric non-local potential and one-dimensional Schrodinger equation with a position-dependent effective mass. Second, we show that the quantum Hamiltonian for a particle with position-dependent mass after applying Liouville–Green transformations will be converted to a quantum Hamiltonian for a particle with constant mass.