Superintegrable systems with position dependent mass

DOI10.1063/1.4908107zbMath1311.81119arXiv1406.2006OpenAlexW2014172116MaRDI QIDQ5250066

T. M. Zasadko, Anatolia G. Nikitin

Publication date: 15 May 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.2006

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Exactly and quasi-solvable systems arising in quantum theory (81U15) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items

Symmetries of Schrödinger–Pauli equations for charged particles and quasirelativistic Schrödinger equations ⋮ Superintegrable quantum mechanical systems with position dependent masses invariant with respect to three parametric Lie groups ⋮ Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups ⋮ Semiconductor quantum wells with BenDaniel–Duke boundary conditions: approximate analytical results ⋮ Fourth order superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials ⋮ Kinematical invariance groups of the 3d Schrödinger equations with position dependent masses ⋮ Advances in QED with intense background fields ⋮ The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass ⋮ Superintegrable relativistic systems in scalar background fields ⋮ Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials ⋮ An inclusive SUSY approach to position dependent mass systems ⋮ Symmetries of the Schrödinger–Pauli equation for neutral particles ⋮ Supersymmetries in Schrödinger–Pauli Equations and in Schrödinger Equations with Position Dependent Mass ⋮ Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations ⋮ Behavior of a constrained particle on superintegrability of the two-dimensional complex Cayley-Klein space and its thermodynamic properties ⋮ Group classification of Schrödinger equations with position dependent mass ⋮ Superintegrable and scale-invariant quantum systems with position-dependent Mass ⋮ Symmetries of Schrödinger equation with scalar and vector potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamical equations, invariants and spectrum generating algebras of mechanical systems with position-dependent mass
• An exactly solvable deformation of the Coulomb problem associated with the Taub-NUT metric
• A family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum
• Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
• Generalized Killing tensors of arbitrary rank and order
• The complete set of symmetry operators of the Schrödinger equation
• Quadratic algebra approach to an exactly solvable position-dependent mass Schrödinger equation in two dimensions
• Exact solvability of superintegrable systems
• Superintegrable systems with spin invariant with respect to the rotation group
• Classical and quantum superintegrability with applications
• HIGHER-ORDER SUSY, EXACTLY SOLVABLE POTENTIALS, AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS
• Integrability and supersymmetry of Schrödinger-Pauli equations for neutral particles
• Matrix superpotentials and superintegrable systems for arbitrary spin
• Laplace–Runge–Lenz vector with spin in any dimension
• Superintegrable systems with spin and second-order integrals of motion
• SUPERINTEGRABLE QUANTUM OSCILLATOR AND KEPLER-COULOMB SYSTEMS ON CURVED SPACES
• Integrable and superintegrable systems with spin
• Superintegrable and shape invariant systems with position dependent mass
• Integrable and superintegrable systems with spin in three-dimensional Euclidean space
• Group theory of the Smorodinsky–Winternitz system
• A systematic study on the exact solution of the position dependent mass Schr dinger equation
• Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem
• New exactly solvable systems with Fock symmetry
• An exactly solvable Schrödinger equation with finite positive position-dependent effective mass
• Laplace-Runge-Lenz vector for arbitrary spin
• Quantum superintegrable systems for arbitrary spin