Exact S-Wave Solution of the Trigonometric Poschl-Teller Potential
M. Hamzavi, A. A. Rajabi
TL;DR
This paper derives exact analytical s-wave solutions for the radial Schrödinger equation with the trigonometric Pöschl-Teller potential, providing explicit energy eigenvalues and eigenfunctions, useful for molecular vibration studies.
Contribution
It presents the first exact analytical solutions for the s-wave Schrödinger equation with the trigonometric Pöschl-Teller potential using the Nikiforov-Uvarov method.
Findings
Closed-form energy eigenvalues obtained.
Explicit eigenfunctions derived.
Numerical results illustrating the solutions.
Abstract
The trigonometric P\"oschl-Teller (PT) potential describes the diatomic molecular vibration. By using the Nikiforov-Uvarov (NU) method, we have obtained the exact analytical s-wave solutions of the radial Schr\"odinger equation (SE) for the trigonometric PT potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented too.
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