Abstract
In this work, we study superintegrable quantum systems in two-dimensional Euclidean space and on a complex two-sphere 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 Schrödinger equation.
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