Analytical Solutions of the Schrödinger Equation with Generalized Hyperbolic Cotangent Potential for Arbitrary l States Via the New Quantization Rule.

The quantum system behaviour in the presence of a potential is best described by the Schrödinger equation. Maturation of analytical methods in solving the Schrödinger equation for various potentials provides a theorist with powerful tools for better understanding the behaviour of quantum systems. With this objective in mind, this paper introduces a novel potential, called the generalized hyperbolic cotangent potential. This potential is interesting because it encompasses a few exponential-type potentials. A quantum system interacting with such a potential, therefore, warrants careful study. The paper presents analytical solutions to the bound state problem of the generalized hyperbolic cotangent potential for arbitrary l states using a newly established quantization rule. Towards this end, the analytical formula is derived for the energy eigenvalue and respective eigenstate. Special cases of the analytical formula of the energy spectrum are discussed for the generalized hyperbolic cotangent potential. [ABSTRACT FROM AUTHOR]