A SU(1,1) Algebraic Method Applied To One-dimensional Physical Models In Quantum Mechanics

Exactly solvable quantum mechanical potentials have attracted much attention since the early days of quantum mechanics, and the Schrodinger Equation has been solved for a large number of potentials by employing a variety of approaches. Among those methods, Lie algebraic method has been the subject of the huge interest in quantum mechanics. It provides a new way and powerful technique to obtain energy eigenvalues and eigenfunctions for some solvable physical systems without dealing with the Schrodinger equations. In particular, an SU(1,1) algebraic method is widely applied to many quantum mechanical models.We construct different realizations of SU(1,1) algebra depending on different potentials. An SU(1,1) algebraic method is proposed in order to obtain the eigenvalues and eigenfunctions of some one-dimenshional solvable potentials. This method shows Cartan operator Ko, the lowering operator K_and the raising operator K+determine successfully energy eigenvalues, the lowest energy eigenfunction and excited energy eigenfunctions respectively.