Eigensolution and Expectation Values of the Hulthen and Generalized Inverse Quadratic Yukawa Potential

Abstract

In this study, the Schrödinger equation was solved with a superposition of the
Hulthen potential and generalized inverse quadratic Yukawa potential model using the
Nikiforov-Uvarov (NU) method. For completeness, we also calculated the wave function.
To validate our results, the numerical bound state energy eigenvalues was computed for
various principal ݊ and angular momentum ℓ quantum numbers. With the aid of the
Hellmann-Feynman theorem, the expressions for the expectation values of the square of
inverse of position, ିݎଶ, inverse of position, ିݎଵ, kinetic energy, ܶ ෠ and square of
momentum, ݌ො are calculated. By adjusting the potential parameters, special cases of the
potential were considered, resulting in Generalized Inverse Quadratic Yukawa potential,
Hulthen potential, Coulomb potential, Kratzer potential, Inversely Quadratic Yukawa
potential and Coulomb plus inverse square potential, respectively. Their energy eigenvalue
expressions and numerical computations agreed with the literature.

PACS: 03.65.−w, 03.65.Ca, 03.65.Ge