First-order intertwining operators and position-dependent mass Schrödinger equations in d dimensions

2005/08/31 by C. Quesne · 9 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #quant-ph

paper · pdf · doi:10.1016/j.aop.2005.11.013

published as Ann. Phys. (N.Y.) 321 (2006) 1221-1239 · 25 pages, no figure, 1 paragraph added in section 4, 1 additional reference

arxiv created 2005/11/03 · openalex publication_date 2006/01/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The problem of d-dimensional Schrodinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H, H₁) of intertwined Hamiltonians one can associate another pair of second-order partial differential operators (R, R₁), related to the same intertwining operator and such that H (resp. H₁) commutes with R (resp. R₁). This property is interpreted in superalgebraic terms in the context of supersymmetric quantum mechanics (SUSYQM). In the two-dimensional case, a solution to the resulting system of partial differential equations is obtained and used to build a physically-relevant model depicting a particle moving in a semi-infinite layer. Such a model is solved by employing either the commutativity of H with some second-order partial differential operator L and the resulting separability of the Schrodinger equation or that of H and R together with SUSYQM and shape-invariance techniques. The relation between both approaches is also studied.

Citations

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

Cited by

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• (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
• Applications of the potential algebras of the two-dimensional Dirac-like operators
• Coherent state of a nonlinear oscillator and its revival dynamics
• A new effective mass Hamiltonian and associated Lamé equation: bound states