SUSY-nonrelativistic quantum eigenspectral energy analysis for squared-type trigonometric potentials through Nikiforov-Uvarov formalism

Explicit and analytical bound-state solutions of the Schrödinger equation for squared-form trigonometric potentials within the framework of supersymmetric quantum mechanics (SUSYQM) are performed by implementing the Nikiforov-Uvarov (NU) polynomial procedure. The first step requires a certain action to adopt an appropriate ansatz superpotential 𝑊(𝑥) for generating the potential pair as 𝑉±(𝑥). In the second process, inserting each potential for the one-dimensional Schrödinger equation and solving the hypergeometric differential equation with the NU-method gives rise to normalized wave function descriptions and algebraically corresponds to the characteristic SUSY quantum energy eigenspectrum sets. It is remarkable to note that, when examined parametrically, they are of reliable and applicable forms concerning the mathematical treatment of various physical quantum systems prescribed in relativistic or nonrelativistic contexts. (author)