MEAN KINETIC ENERGY OF A SYSTEM IN A MORE GENERALIZED HULTHÉN POTENTIAL WELL

Eyube E.S1., Adamu A.D.2 and Adamu J.3

1, 2Department of Physics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria

3Physics Unit, Department of Physical Sciences Education, School of Technology and Science Education, Modibbo Adama University of Technology, Yola Nigeria

Abstract

In this paper we have obtained the analytical solutions of Schrödinger equation with the more generalized Hulthén potential well within the confines of improved quantization rule to derive closed form expressions for bound states energy eigenvalues and radial eigenfunctions, to ensure an all wave solutions satisfying ℓ ≥ 0, a Pekeris-like approximation model was applied to deal with the centrifugal term potential of the Schrödinger equation. Special case of s-wave eigen energies and eigenfunctions were deduced, the results we obtained are in perfect agreement with exact solutions of the Schrödinger equation for the deformed Hulthén potential in the literature. We have applied our expression for eigen energies to derive expression for mean kinetic energy of a system in a more generalized Hulthén potential well. For arbitrary principal and angular momentum quantum numbers and potential parameter q, we have computed bound states energy eigenvalues and mean kinetic energy in natural units, studies show that for small values of screening parameters, both eigen energy and mean kinetic energy tend to increase approximately linearly for small values of q and remains fairly constant in the region of zero for large values of q

Keywords: Kinetic energy, potential energy, expectation values, Hellmann-Feynman theorem, improved quantization rule