A New Approach to the Exact Solutions of the Effective Mass Schrödinger Equation

Abstract

Effective mass Schrödinger equation is solved exactly for a given potential. NikiforovUvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrödinger equation is also solved for the Morse potential transforming to the constant mass Schrödinger equation for a potential. One can also get solution of the effective mass Schrödinger equation starting from the constant mass Schrödinger equation.

Exact solutions of the position-dependent-effective mass Schrödinger equation

“…[42][43][44] We can cite the point-canonical transformation, 24,25,45,46 Nikiforov-Uvarov (NU) method [45][46][47][48][49] Green's function, 50 the Heun equation, 51 the potential algebra 52 and the supersymmetric approach 53,54 as analytical methods to generate solutions for the PDEM Schrödinger equation. However, the exact solutions are limited to a small set of systems.…”

Analytical Solution of the Schrödinger Equation with Spatially Varying Effective Mass for Generalised Hylleraas Potential

“…Several authors have studied the effects of the position-dependent mass on the solutions of the Schrödinger equation. A positiondependent effective mass, ( ) = 1 ⋅ ( ), associated with a quantum mechanical particle constitutes a useful model for the study of various potentials such as Morse potential [12][13][14][15][16][17][18], hard-core potential [18], Scarf potential [19][20][21], Pöschl-Teller potential [22,23], spherically ring-shaped potential [24], Hulthén potential [25], Kratzer potential [26], and Coulomb-like potential [27,28]. Different techniques have been developed to obtain its exact solutions, such as factorization methods [29], Nikiforov-Uvarov (NU) methods [30], and supersymmetric quantum mechanics [31].…”

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

“…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.…”