2006/12/12 by C. Quesne, Quesne, C.
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.quant-ph/0612094
openalex publication_date 2006/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. Finally, the two-dimensional model is extended to two integrable and exactly solvable (but not superintegrable) models in three dimensions, depicting a particle in a semi-infinite parallelepipedal or cylindrical channel, respectively.