2000 character limit reached
Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 1. Systems with cylindric symmetry
Published 2 Mar 2024 in math-ph and math.MP | (2403.01235v3)
Abstract: Cylindrically symmetric quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion are classified. It is proved that there exist 68 such systems which are inequivalent. Among them there are twenty seven superintegrable and twelve maximally superintegrable. The arbitrary elements of the correspondinding Hamiltonians (i.e.,masses and potentials) are presented explicitly.
- N. Evans. Group theory of the Smorodinsky-Winternitz system. J. Math. Phys. 32, 3369-3375 (1991).
- N. W. Evans. Super-integrability of the Winternitz system. Phys. Lett. 147, 483-486 (1990).
- P. Winternitz and I. Yurdusen. Integrable and superintegrable systems with spin. J. Math. Phys. 47 103509 (2006).
- J. -F. Désilets, P. Winternitz and I. Yurdusen. Superintegrable systems with spin and second-order integrals of motion. Phys. A: Math. Theor. 45 475201 (2012).
- A. G. Nikitin. New exactly solvable systems with Fock symmetry. J. Phys. A: Math. Theor. 45 485204 (2012)
- A. G. Nikitin. Matrix superpotentials and superintegrable systems for arbitrary spin J. Phys. A: Math. Theor. 45 225205 (2012)
- von Roos O Position-dependent effective masses in semiconductor theory Phys. Rev. B 27, 7547–7552 ( 1983).
- A. G. Nikitin, Superintegrable quantum mechanical systems with position dependent masses invariant with respect to three parametric Lie groups. J. Math. Phys. DOI: 1063/5.0147792
- . A. G. Nikitin. Superintegrable and shape invariant systems with position dependent mass. J. Phys. A: Math. Theor. 48, 335201 (2015)
- J. Hietarinta, Pure quantum integrability Phys. Lett. A 246 97-104 (1998).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.