Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem

2004/03/23 by C. Quesne, V. M. Tkachuk · 16 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #math.QA #quant-ph

paper · pdf · doi:10.1088/0305-4470/37/14/006

published as J.Phys.A37:4267-4281,2004 · 22 pages, no figure. Archive version is already official. Published by JPA at http://stacks.iop.org/0305-4470/37/4267

openalex publication_date 2004/03/23 · arxiv created 2004/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We show that there exist some intimate connections between three unconventional Schrödinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space. This occurs whenever a specific relation between the deforming function, the position-dependent mass and the (diagonal) metric tensor holds true. We illustrate these three equivalent approaches by considering a new Coulomb problem and solving it by means of supersymmetric quantum mechanical and shape invariance techniques. We show that in contrast with the conventional Coulomb problem, the new one gives rise to only a finite number of bound states.

Citations

• Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations
• Supersymmetry and Quantum Mechanics
• Superintegrable systems in Darboux spaces
• Superintegrability in a two-dimensional space of nonconstant curvature

Cited by

• Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels
• Oscillator-Morse–Coulomb mappings and algebras for constant or position-dependent mass
• Analytical Solutions to the Klein–Gordon Equation with Position-Dependent Mass for q -Parameter Pöschl–Teller Potential
• A singular position-dependent mass particle in an infinite potential well
• First-order intertwining operators and position-dependent mass Schrödinger equations in d dimensions
• On Two Superintegrable Nonlinear Oscillators in N Dimensions
• Comparison Theorems for the Position-Dependent Mass Schrödinger Equation
• Ordering ambiguity versus representation
• First-Order Intertwining Operators with Position Dependent Mass and η-Weak-Pseudo-Hermiticity Generators
• (1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively PT -Symmetric
• Energy-Levels Crossing and Radial Dirac Equation: Supersymmetry and Quasi-Parity Spectral Signatures
• Coherent state of a nonlinear oscillator and its revival dynamics
• A new effective mass Hamiltonian and associated Lamé equation: bound states
• Global versus local superintegrability of nonlinear oscillators
• COHERENT STATE OF THE EFFECTIVE MASS HARMONIC OSCILLATOR
• Radial power-law position-dependent mass: cylindrical coordinates, separability and spectral signatures