Scattering and bound state solutions of the asymmetric Hulthén potential

Abstract

One-dimensional time-independent Schrödinger equation is solved for the asymmetric Hulthén potential. Reflection and transmission coefficients and bound state solutions are obtained in terms of the hypergeometric functions. It is observed that the unitary condition is satisfied in nonrelativistic region.

Scattering of a spinless particle by an asymmetric Hulthén potential within the effective mass formalism

“…[9]. After these pioneering studies, the transmission resonance and supercriticality for the relativistic/non-relativistic particles in an external potentials have been extensively discussed [3,11,12,13,14,15,16,17,18]. In one of these studies [13], the authors showed that the transmission coefficient obtained for the Klein-Gordon particle displays a behavior similar to that of the one obtained for the Dirac particle [8].…”

A new model for calculating the binding energy of the lithium nucleus under the generalized Yukawa potential and Hellmann potential

“…It has many applications in atomic physics and condensed-matter physics [14][15][16][17][18][19][20][21][22][23][24]. The Hellmann potential, with 0 V positive, was suggested originally by Hellmann [15,25] and henceforth called the Hellmann potential if 0 V is positive or negative. The Hellmann potential was used as a model for alkali hydride molecules [17].…”

Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential

“…Analytic solutions have been obtained for the the square well [2,3], Woods-Saxon potential [4], cusp potential [5], and Hulthén potential [6] as well as asymmetric barriers [7,8], multiple barriers [9], and a class of short-range potentials [10]. The successful isolation of graphene [11] has led to renewed interest in the transmission-reflection problem for the one-dimensional Dirac equation.…”