The solution of integro-differential Schrodinger equation (IDSE)whichwas 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 onedimensional Schrodinger equationwith a position-dependent effectivemass. Second, we showthat 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.
