Analytic Results in the Position-Dependent Mass Schrödinger Problem

Abstract

We investigate the Schrodinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V (x) = 0 case whose solutions are hypergeometric functions in tanh 2 x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V (x) = V0 sinh 2 x. *

Torsion effects on a relativistic position-dependent mass system

“…At present days, several discussions can be found in the literature with the purpose of showing different ways of dealing with position dependent-mass systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Another context has been discussed in Ref.…”

Energy eigenfunctions for position-dependent mass particles in a new class of molecular Hamiltonians

“…For some relevant mass distributions some phenomenological potentials have been solved in recent years. [21][22][23][24][25][26][27][28] The origin of the PDM approximation can be traced back in the domain of solid state physics. [29][30][31][32][33][34][35][36] For instance, the dynamics of electrons in semiconductor heterostructures has been tackled with an effective mass model related to the envelope-function approximation.…”

Effect of Intense Laser Field in Gaussian Quantum Well With Position‐Dependent Effective Mass

“…Within the framework of the effective mass approximation, the position dependent mass Schrödinger equation can be given by where m ( z ) is the electron PDM and V ( z ) is the QW Gaussian potential which is defined as follows: …”

“…Also, it has been shown that the developed model can be easily expanded to semiconductor heterostructures . The effect of spatially dependent effective mass in QW structures has become of increasing experimental and theoretical interest . The effects of the position‐dependent effective mass on the optical properties in parabolic QWs have been calculated by Herling and Rustgi, and they have stated that the bound energy levels are lowered with respect to those with constant effective mass .…”

“…[39] The effect of spatially dependent effective mass in QW structures has become of increasing experimental [40] and theoretical interest. [41][42][43][44][45][46][47][48][49][50][51][52][53][54] The effects of the positiondependent effective mass on the optical properties in parabolic QWs have been calculated by Herling and Rustgi, and they have stated that the bound energy levels are lowered with respect to those with constant effective mass. [41] Influence of the PDM on donor binding energy in a square and V-shaped QWs in the presence of a magnetic field has been calculated variationally by Panahi et al [43] It was found that the PDM impurity binding energy is larger than the one with a constant effective mass, and this effect is more prominent in narrow wells.…”