Deformed oscillator algebra for quantum superintegrable systems in two-dimensional Euclidean space and on a complex two-sphere

摘要

In this work,we study superintegrable quantum systems in two-dimensional Euclidean space and on a complex twosphere with second-order constants of motion.We show that these constants of motion satisfy the deformed oscillator algebra.Then,we easily calculate the energy eigenvalues in an algebraic way by solving of a system of two equations satisfied by its structure function.The results are in agreement to the ones obtained from the solution of the relevant Schr(o)dinger equation.