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… 

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

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

  • A. Moreira
  • Physics
    Journal 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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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
...