Abstract

EDET, C.O. et al. Solutions of Schrödinger equation and thermal properties of generalized trigonometric Pöschl-Teller potential. Rev. mex. fis. [online]. 2020, vol.66, n.6, pp.824-839.  Epub Jan 31, 2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.66.824.

Analytical solutions of the Schrödinger equation for the generalized trigonometric Pöschl-Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the partition function was calculated, and other relevant thermodynamic properties. More so, we use the concept of superstatistics to evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter (q = 0), and this is displayed graphically for the clarity of our results. We also obtain the normalized wave function in terms of the hypergeometric function. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Pöschl-Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods.

Keywords : Trigonometric Pöschl-Teller potential; factorization method; superstatistics; Schrödinger equation.