Analytical solution to position dependent mass Schrödinger equation

Abstract

Using a recently developed technique to solve Schrödinger equation for constant mass, we studied the regime in which mass varies with position i.e position dependent mass Schrödinger equation(PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass $m(x)$ particle scattered by a potential $\mathcal{V}(x)$. We also studied the structural analogy between PDMSE and two-level atomic system interacting with a classical field.

5 pages, 4 figures

References in corpus (8)

• Effective Mass of One 4he Atom in Liquid 3he
• Solutions of the nonrelativistic wave equation with position-dependent effective mass
• Coherent control of atomic excitation using off-resonant strong few-cycle pulses
• Treating some solid state problems with the Dirac equation
• Coherent Excitation of a Two-Level Atom driven by a far off-resonant Classical Field: Analytical Solutions
• Analytical solutions for a two-level system driven by a class of chirped pulses
• A Group-Theoretical Method for Natanzon Potentials in Position-Dependent Mass Background
• Potential algebra approach to position dependent mass Schroedinger equation

Cited by in corpus (8)

• The transfer matrix: a geometrical perspective
• Matrix algorithm for solving Schroedinger equations with position-dependent mass or complex optical potentials
• Scattering states of a particle, with position-dependent mass, in a double heterojunction
• On the position dependent effective mass Hamiltonian
• Ultra-short strong excitation of two-level systems
• Solitons supported by intensity-dependent dispersion
• Goldilocks Probes for Noisy Interferometry via Quantum Annealing to Criticality
• Non-standard quantum algebras and infinite-dimensional PT-symmetric systems