2014/12/31 by A. G. Nikitin · 25 citations
Mathematics · Physics and Astronomy · #Economics #Integrable system #Invariant (physics) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Position (finance) #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP #msc:0230IK #msc:0365GE #msc:1130PB #quant-ph
paper · pdf · doi:10.1088/1751-8113/48/33/335201
published in Journal of Physics A Mathematical and Theoretical 48(33), 335201 (Institute of Physics) · misprints are corrected and discussion is extended
arxiv created 2015/06/29 · openalex publication_date 2015/07/24 · arxiv updated 2016/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least 1 second order integral of motion. All such systems appear to be also shape invariant and exactly solvable. Moreover, some of them possess the property of double shape invariance and can be solved using two different superpotentials. Among them there are systems with double shape invariance which present nice bridges between the Coulomb and isotropic oscillator systems. A simple algorithm for calculating the discrete spectrum and the corresponding state vectors for the considered PDM systems is presented and applied to solve five of the found systems.