Radial power-law position-dependent mass: cylindrical coordinates, separability and spectral signatures

2011/04/07 by Omar Mustafa · 3 citations
Mathematics · Physics and Astronomy · #Atomic and Molecular Physics #Azimuth #Harmonic #Harmonic oscillator #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Radial function #Radial velocity #Symmetry (geometry) #Symmetry in biology #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/1751-8113/44/35/355303

published as J. Phys. A: Math. Theor. 44, 355303 (2011) · 17 pages

arxiv created 2011/04/07 · openalex publication_date 2011/08/10 · arxiv updated 2011/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We discuss the separability of the position-dependent-mass (PDM) Hamiltonian in cylindrical coordinates in the framework of a radial power-law PDM. We consider two particular radial mass settings: a harmonic oscillator type and a Coulombic type. We subject the radial harmonic oscillator-type mass to a radial harmonic oscillator potential and the radial Coulombic mass to a radial Coulombic potential. Azimuthal symmetry is assumed and spectral signatures of various z -dependent interaction potentials are reported.

Citations

• Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem
• Ordering Ambiguity Revisited via Position Dependent Mass Pseudo-Momentum Operators
• Ordering ambiguity versus representation
• A singular position-dependent mass particle in an infinite potential well
• First-order intertwining operators and position-dependent mass Schrödinger equations in d dimensions

Cited by

• Position-Dependent Mass Systems: Classical and Quantum Pictures
• Landau quantization for an electric quadrupole moment of position-dependent mass quantum particles interacting with electromagnetic fields
• n -dimensional PDM non-linear oscillators: linearizability and Euler–Lagrange or Newtonian invariance