Analytical Approximations to the Schrödinger Equation for a Second Pöschl–teller-Like Potential With Centrifugal Term

Abstract

The bound state solutions of the Schrödinger equation for a second Pöschl-Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2 F 1 (a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V 1 = V 2 are also studied briefly.

The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term

“…Therefore, we must use a proper approximation for the centrifugal term similar to other authors. Unlike the following approximation used in the previous work [7][8][9][10][11][12][24][25][26],…”

“…For example, some authors have approximately solved the Schrödinger and Klein-Gordon equations for some po-tentials, these potentials include the Manning-Rosen potential [7], the Eckart potential [8], Hulthén potential [9], the Pöschl-Teller potential [10], etc. Based on previous work [7][8][9][10], we have applied a proper approximation to the centrifugal term to obtain approximately analytical −wave scattering solutions of the Schrödinger equation with the Manning-Rosen potential [11], the Eckart potential [12] and −wave bound solutions with the second Pöschl-Teller like potential [13] and the the hyperbolical potential [14] within the frame work of non-relativistic and relativistic quantum mechanics. The Manning-Rosen potential is an importantly solvable exponential-type potential describing diatomic molecules in quantum mechanics.…”

Tensor coupling and relativistic spin and pseudospin symmetries of the Pöschl–Teller-like potential

“…The potential parameters V 1 and V 2 describe the property of the potential well, V 1 [ V 2 , while a is related to the range of the potential [19][20][21][22][23][24]. The behavior of this potential with respect to four different values of a is shown in Fig.…”

A General Approach for the Exact Solution of the Schrödinger Equation

“…These potentials are Morse [41], Rosen-Morse [42][43][44], Pseudoharmonic [45,46], Mie [47][48][49][50][51][52][53][54], Woods-Saxon [55][56][57][58][59][60][61], Poschl-Teller [62][63][64][65][66], Kratzer-Fues [67,68], Noncentral [69][70][71][72]. Woods-Saxon potential describes the interaction of a neutron with a heavy nucleus.…”