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In this paper, time-dependent Schrödinger equation is considered with the Pöschl–Teller double-ring shaped harmonic potential. Then, for investigation of such a system, the Lewis–Riesenfeld dynamical invariant method is presented and shown that how it works. After that, the form and eigenfunctions for the Lewis-Riesenfeld dynamical invariant are derived and the exact solutions are studied. Then the physical interpretations of derived results are discussed.

Exact Solutions for Time-Dependent Schrödinger Equation in Presence of the Pöschl-Teller Double-Ring Shaped Harmonic Potential