Bound states of the Dirac equation with some physical potentials by the Nikiforov–Uvarov method

Abstract

Exact analytical solutions for the s-wave Dirac equation with the reflectionless-type, Rosen–Morse and Manning–Rosen potentials are obtained, under the condition of spin symmetry. We obtained bound state energy eigenvalues and corresponding spinor wave function in the framework of the Nikiforov–Uvarov (NU) method.

Approximate bound states of the Dirac equation with some physical quantum potentials

“…The exact solutions of the Dirac equation for the exponential-type potentials are possible only for the s-wave (κ = ±1 case) when the spin-orbit coupling term will get suppressed [34]. However, for l-states an approximation scheme has to be used to deal with the spinorbit centrifugal κ(κ + 1)/r 2 (pseudo-centrifugal, κ(κ − 1)/r 2 ) term.…”

“…The aim of the present paper is to extend the s-wave solutions by solving the Dirac equation with some physical potentials given in Ref. [34] in the framework of the Nikiforov-Uvarov (NU) method [46][47][48][49][50] by taking an approximation to deal with the centrifugal (pseudocentrifugal) potential term [20,51]. The approximation scheme used to deal with the spinorbit centrifugal barrier κ(κ + 1)/r 2 holds for values of spin-orbit coupling quantum number κ that are not large and vibrations of the small amplitude [51].…”

An Algebraic Approach to the Kemmer Equation for Dirac Oscillator

“…By using Nikiforov-Uvarov mathematical method [12][13][14][15] one can easily obtain the exact solution of (9) as…”

Analytical Solution of a Wave Equation in Cosmology

“…Using the solutions of these equations we obtain a wave equation based on a null condition describing universe expansion. For solving this equation, first we briefly review Nikiforov-Uvarov mathematical method [6][7][8][9][10][11][12][13][14][15][16]. This method provides analytical solutions of the generalized equation of hypergeometric type.…”