Comprehensive treatments for Schrödinger equations involving constant and non-constant masses

The concept of the elegant work introduced by Lévai in Ref. [21] is extended for the solutions of the Schrödinger equation with more realistic other potentials used in different disciplines of physics within the constant mass consideration. The connection between the present model and the other alternative algebraic technique [32] in the literature is discussed in detail. Extending the point canonical transformation approach introduced in this thesis in a manner distinct from the previous ones, we also propose a unified approach of generating potentials of all classes having non-constant masses.