Analytical Solution of Schrödinger's Equation Subject to Pöschl-Teller's Potential
Abstract - The Schrödinger's equation plays a fundamental role in quantum mechanics and its study involves the knowledge of techniques for solving of differential equations. When submitted to the Pöschl-Teller's potential, the time-independent equation has nonlinear coefficients and, in this research, the analytical solution was proposed. After substitution of variables, the problem was modeled by the Gauss's equation with the resolution presented in terms of the coefficients and of the hypergeometric function. The exposed study can be reproduced in courses of the area and presents the relevance of the development of differential equations applied to quantum mechanics.
Keywords - Quantum mechanics, Hypergeometric equation, Differential equations.