Morse potential and its relationship with the Coulomb in a position-dependent mass background

Abstract

We provide some explicit examples wherein the Schrödinger equation for the Morse potential remains exactly solvable in a position-dependent mass background. Furthermore, we show how in such a context, the map from the full line $(-\infty ,\infty )$ to the half line $(0,\infty )$ may convert an exactly solvable Morse potential into an exactly solvable Coulomb one. This generalizes a well-known property of constant-mass problems.

9 pages, no figure; final published version

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Cited by in corpus (12)

• Rotation and vibration of diatomic molecule in the spatially-dependent mass Schrodinger equation with generalized q-deformed Morse potential
• Position Dependent Mass Oscillators and Coherent States
• Exact Klein-Gordon equation with spatially-dependent masses for unequal scalar-vector Coulomb-like potentials
• Approximate Analytical Solutions of the Klein-Gordon Equation for Hulthen Potential with Position-Dependent Mass
• Exact solution of Effective mass Schrodinger Equation for the Hulthen potential
• Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
• Solutions of N-dimensional Schrödinger Equation with Morse Potential Via Laplace Transforms
• A new approach to the exact solutions of the effective mass Schrodinger equation
• The Quantum Effective Mass Hamilton-Jacobi Problem
• Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass
• New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential
• Exact solution of Schrödinger equation for the complex Morse potential to investigate physical systems with position-dependent complex mass