Exactly Solvable Effective Mass D-Dimensional Schrödinger Equation for Pseudoharmonic and Modified Kratzer Problems

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

“…In addition, the authors of Refs. [44][45][46] approximated the centrifugal potential term [17-19, 73, 74] where C = ( + 1)α 2 [36][37][38][39][40]. However, in the present work, Eq.…”

“…The NU method has been used to solve the Schrödinger [34,35], KG [36][37][38][39][40]61] and Dirac 1 [55] wave equations for central and non-central potentials. Let us briefly outline the basic concepts of the method [62].…”

“…Thus the associated uppercomponent F κ ( ) for arbitrary the spin-orbit coupling quantum number κ can be obtained by substituting Eqs. (39) and (41) into Eq. (2) as (43) with which the corresponding lower component G κ ( ) can be given by solving Eq.…”

“…For some potentials, relativistic solutions have recently been found. For example, the bound-state solution of the KG equation for the vector and scalar general Hulthén-type [9] and Rosen-Morse-type [14] potentials with any arbitrary -state, the position-dependent effective mass KG equation for scalar and vector Hulthén potentials in any arbitrary dimension D and orbital quantum number using the NU method combined with a new approximation scheme for the centrifugal potential term [36][37][38][39][40] and the 1D Dirac [10] and spinless Salpeter [15] equations with -symmetric real and complex forms of generalized Hulthén potentials.…”

Complete Analytical Solutions of the Mie-Type Potentials in N-Dimensions

“…The Mie-type potential, which is a diatomic potential, has been studied using methods such as the NikiforovUvarov Method [10], polynomial method [11][12][13][14], the ansatz wave function method [15][16][17]20] and the 1/N expansion method [33]. Generally, one can define the Mie-type potential as [13,34]:…”