Exact Solution of Effective Mass Schrödinger Equation for the Hulthen Potential

Abstract

A general form of the effective mass Schrödinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function.

Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

“…Bound state solutions of relativistic and nonrelativistic wave equation arouse a lot of interest for decades. Schrodinger wave equations constitute nonrelativistic wave equation while Klein-Gordon and Dirac equations constitute the relativistic wave equations [6][7][8][9][10]. Bound state solutions predominantly have negative energies because the energy of the particle is less than the maximum potential energy [11].…”

Solutions of Schrödinger Equation with Generalized Inverted Hyperbolic Potential

“…The Nikiforov-Uvarov (NU) method, [20] was proposed and applied to reduce the second order differential equation to the hypergeometric-type equation by an appropriate co-ordinate transformation S = S(r) as, [15,20].…”

“…for a given potential [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. It is well known that these solutions play an essential role in the relativistic and non-relativistic quantum mechanics for some physical potentials of interest, [1,2,12,[17][18][19].…”

Generation of Exactly Solvable Potentials of Position-Dependent Mass Schrödinger Equation from Hulthen Potential

“…We have considered Hulthen potential as a typical representative of an exactly solved quantum system whose exact solution of 1D-PDM Schrödinger equation is available/possible [12]. The deformed Hulthen potential, denoted as V A (x) is given by…”

“…Such studies use different methods known for solving constant mass Schrödinger equations or an extension of them. Point Canonical Transformation (PCT) [6][7][8][9][10], Nikiforov-Uvarov (NU) method [11][12][13], Supersymmetry (SUSY) quantum mechanics approach [14,15], Quadratic Algebra [16], Darboux Transformation (DT) [17,18] etc. are different approaches used in the study of PDM Schrödinger equations.…”