Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups

DOI10.1088/1751-8121/acee2farXiv2304.00638MaRDI QIDQ6096906

Anatolia G. Nikitin

Publication date: 15 September 2023

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

Full work available at URL: https://arxiv.org/abs/2304.00638

zbMATH Keywords

equivalencemaximalresultsaccordancesi.e. position dependent masspresented

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (1)

Superintegrable quantum mechanical systems with position dependent masses invariant with respect to three parametric Lie groups

Cites Work

• Unnamed Item
• Unnamed Item
• A family of exactly solvable radial quantum systems on space of non-constant curvature with accidental degeneracy in the spectrum
• Superintegrable oscillator and Kepler systems on spaces of nonconstant curvature via the Stäckel transform
• Generalized Killing tensors of arbitrary rank and order
• The complete set of symmetry operators of the Schrödinger equation
• An algebraic geometric classification of superintegrable systems in the Euclidean plane
• Pure quantum integrability
• Stäckel equivalence of non-degenerate superintegrable systems, and invariant quadrics
• Superintegrable and scale-invariant quantum systems with position-dependent Mass
• Toward classification of 2nd order superintegrable systems in 3-dimensional conformally flat spaces with functionally linearly dependent symmetry operators
• Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials
• Doubly exotic \(N\)th-order superintegrable classical systems separating in Cartesian coordinates
• Completeness of superintegrability in two-dimensional constant-curvature spaces
• Group classification of Schrödinger equations with position dependent mass
• Matrix superpotentials and superintegrable systems for arbitrary spin
• Invariant classification of second-order conformally flat superintegrable systems
• Toward a classification of semidegenerate 3D superintegrable systems
• Superintegrable systems with spin and second-order integrals of motion
• Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems
• GeneralNth order integrals of motion in the Euclidean plane
• 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
• Superintegrability with third-order integrals in quantum and classical mechanics
• Hamiltonians separable in Cartesian coordinates and third-order integrals of motion
• Symmetries of the Schrödinger–Pauli equation for neutral particles
• Symmetries of Schrödinger–Pauli equations for charged particles and quasirelativistic Schrödinger equations
• Position-Dependent Mass Systems: Classical and Quantum Pictures
• Superintegrable systems with position dependent mass
• Kinematical invariance groups of the 3d Schrödinger equations with position dependent masses
• New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates
• Symmetries of Schrödinger equation with scalar and vector potentials
• Superintegrability of three-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems
• Superintegrability on the three-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the sphere S ³ and on the hyperbolic space H ³

This page was built for publication: Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups