Methods for solution of Schrödinger equation with position dependent mass (PDM)

In this study, construction of PDM Schrödinger equation has been examined starting from the kinetic energy operator approximations. In addition to this, the role and improvement of the Schrödinger type equations? solutions have been discussed.Some of the most common methods used in order to solve Schrödinger type equations have been explained by using important articles. The potentials and the mass functions used have been emphasized. Also, the opportunity of comparing the studies have been given.To solve PDM Schrödinger equation which has been transformed in the form of the constant mass Schrödinger equation by changing coordinate and wave function is discussed for physical acceptability. Although it was expected to have different results from both of the experiments, the same eigenvalues have been found. This situation caused the improvement of a new method without transformation. The method improved by modifying Taylor Expansion Method is called Asymptotic Taylor Expansion Method.PDM Schrödinger equation has been solved by using Asymptotic Taylor Expansion Method for harmonic oscillator potentials. Asymptotic analyze has been done for four different Hamitonians and highly accurate energy eigenvalues and wavefunctions have been obtained. As a result of this, Asymptotic Taylor Expansion Method has been proved very useful to determine energy eigenvalues and wavefunctions in Schrödinger type equations.