# Analytic Results in the Position-Dependent Mass Schrödinger Problem

@article{Cunha2013AnalyticRI, title={Analytic Results in the Position-Dependent Mass Schr{\"o}dinger Problem}, author={M. S. Cunha and Hugo R. Christiansen}, journal={Communications in Theoretical Physics}, year={2013}, volume={60}, pages={642 - 650} }

We investigate the Schrödinger 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 tanh2 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…

## 36 Citations

### Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials

- Physics, Mathematics
- 2013

We analytically solve the position-dependent mass (PDM) 1D Schrodinger equation for a new class of hyperbolic potentials Vqp(x)=−V0sinhpxcoshqx,p=−2,0,⋯q [see C. A. Downing, J. Math. Phys. 54, 072101…

### Quantum information for a solitonic particle with hyperbolic interaction

- PhysicsJournal of Computational Electronics
- 2021

In this work, we analyze a particle with position-dependent mass, with solitonic mass distribution in a stationary quantum system, for the particular case of the BenDaniel-Duke ordering, in a…

### Exact Solutions of Schrödinger Equation for the Position-Dependent Effective Mass Harmonic Oscillator

- Physics
- 2014

A one-dimensional harmonic oscillator with position-dependent effective mass is studied. We quantize the oscillator to obtain a quantum Hamiltonian, which is manifestly Hermitian in configuration…

### Semi-exact solutions to position-dependent mass Schrödinger problem with a class of hyperbolic potential V0tanh(ax)

- Mathematics
- 2016

Abstract.In this work we report the semi-exact solutions of the position-dependent mass Schrödinger equation (PDMSE) with a class of hyperbolic potential $ V_{0}\tanh(a x)$. The terminology of…

### Exact solution of Schrödinger equation with q-deformed quantum potentials using Nikiforov—Uvarov method

- Physics, Mathematics
- 2013

In this paper, we present the exact solution of the one-dimensional Schrödinger equation for the q-deformed quantum potentials via the Nikiforov—Uvarov method. The eigenvalues and eigenfunctions of…

### Exact solutions to solitonic profile mass Schrödinger problem with a modified Pöschl–Teller potential

- Physics
- 2016

We present exact solutions of solitonic profile mass Schrodinger equation with a modified Poschl–Teller potential. We find that the solutions can be expressed analytically in terms of confluent Heun…

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

- Physics
- 2014

Based on recent results on quasi-exactly solvable Schrodinger equations, we review a new phenomenological potential class lately reported. In the present paper, we consider the quantum differential…

### The exact solution of the Schrödinger equation with a polynomially spatially varying mass

- Physics
- 2017

The Schrodinger equation with a position-dependent mass (SEPDM) is employed in many areas of quantum physics. Exact solutions for the SEPDM lie at the center of interest of the professional public…

## References

SHOWING 1-10 OF 70 REFERENCES

### A general scheme for the effective-mass schrödinger equation and the generation of the associated potentials

- Physics
- 2004

A systematic procedure to study one-dimensional Schrodinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem…

### Algebraic Approach to the Position-Dependent Mass SCHRÖDINGER Equation for a Singular Oscillator

- Mathematics, Physics
- 2007

We construct a singular oscillator Hamiltonian with a position-dependent effective mass. We find that an su(1, 1) algebra is the hidden symmetry of this quantum system and the isospectral potentials…

### Bound State Solutions of Schrödinger Equation for Generalized Morse Potential with Position-Dependent Mass

- Physics
- 2011

The effective mass one-dimensional Schrodinger equation for the generalized Morse potential is solved by using Nikiforov—Uvarov method. Energy eigenvalues and corresponding eigenfunctions are…

### Series solutions of the Schrodinger equation with position-dependent mass for the Morse potential [rapid communication]

- Physics, Mathematics
- 2004

### Exact Solution of the SCHRÖDINGER Equation for the Modified Kratzer's Molecular Potential with Position-Dependent Mass

- Physics
- 2008

Exact solutions of Schrodinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the…

### New Soluble Energy Band Problem

- Physics
- 1958

The Schrodinger equation for V(x) = - V0 csc2(πx/a) is solved. E(k) and the effective mass are examined along with the wave functions for various values of the parameter (V0a2). It is found that the…

### Supersymmetric approach to quantum systems with position-dependent effective mass

- Physics
- 1999

We consider the application of the supersymmetric quantum-mechanical formalism to the Schr\"odinger equation describing a particle characterized by a position-dependent effective mass $m(x).$ We show…

### Bound state solutions of the Manning-Rosen potential

- Physics
- 2012

Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the $\ell$-wave solutions of the Schr\"{o}dinger equation with the Manning-Rosen potential. The equation of…