Special Functions of Mathematical Physics

Relativistic Treatment of Massive Klein-Gordon Particle by Modified Generalized Hulthen Potential

“…When a particle is in a strong potential field, the relativistic effect must be considered, which gives the correction for non relativistic quantum mechanics [14]. In solving non relativistic or relativistic wave equation whether for central or non central potential, various methods are used such as Asymptotic iteration method (AIM) [15], Super symmetric quantum mechanics (SUSYQM) [16] shifted N 1 expansion [17], factorization [18], Nikiforov-Uvarov (NU) *To whom correspondence should be addressed: E-mail: antiacauchy@yahoo.com, akaninyeneantia@uniuyo.edu.ng method [19] etc.…”

“…The conventional NU method was presented by Nikiforov and Uvarov [19] and has been employed to solve second order differential equations such as the Schrödinger, Klein-Gordon and Dirac equations etc. The parametric generalization of the NU method is given by the generalized hyper-geometric type equation as [27] …”

Solution of Dirac Equation with Modified Hylleraas Potential under Spin and Pseudospin Symmetry

“…Recently, many authors have investigated the Dirac equation approximately with spin and pseudospin symmetries for different potential models such as the Hulthen potential [6], generalized Morse potential [7], the Dirac-Hulthen problem [8], Hulthen potential including Coulomb-like tensor potential [9], the Woods-Saxon [10], Relativistic Morse potential [11] and others [12]. The bound state solution of the Dirac equation under spin and pseudospin symmetries have been obtain using various methods such as the supersymmetric quantum mechanics (SUSY) [13], the Nikiforov-Uvarov method [14] and others [15]. Ikot [16]has investigated the Dirac equation with Hyperbolical potential including Coulomb-like tensor potential under spin symmetry for any spin-orbit and the wave functions and the corresponding energy eigenvalue have been calculated using the improved approximation scheme for the centrifugal term κ(κ±1) r 2 .…”

“…The concept of NU method [14] was proposed to solve the second-order linear differential equation by reducing it to a generalized equation of hypergeometric-type of the form…”

Hypergeometric Type Functions and Their Symmetries

“…Our work is strongly inspired by the book by Nikiforov and Uvarov [10], who tried to develop a unified approach to hypergeometric type functions. They stressed, in particular, the role of integral representations and of recurrence relations.…”