Superintegrable systems with a position dependent mass : Kepler-related and Oscillator-related systems

Abstract

The superintegrability of two-dimensional Hamiltonians with a position dependent mass (pdm) is studied (the kinetic term contains a factor $m$ that depends of the radial coordinate). First, the properties of Killing vectors are studied and the associated Noether momenta are obtained. Then the existence of several families of superintegrable Hamiltonians is proved and the quadratic integrals of motion are explicitly obtained. These families include, as particular cases, some systems previously obtained making use of different approaches. We also relate the superintegrability of some of these pdm systems with the existence of complex functions endowed with interesting Poisson bracket properties. Finally the relation of these pdm Hamiltonians with the Euclidean Kepler problem and with the Euclidean harmonic oscillator is analyzed.

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Cited by in corpus (11)

• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
• Information-theoretic measures for a position-dependent mass system in an infinite potential well
• New bi-Hamiltonian systems on the plane
• Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass
• The Kepler problem: polynomial algebra of non-polynomial first integrals
• Transformation of the Stackel matrices preserving superintegrability
• Quasi-exactly solvable extensions of the Kepler-Coulomb potential on the sphere
• Discretization and superintegrability all rolled into one
• Superintegrability of 3-dimensional Hamiltonian systems with conformally Euclidean metrics. Oscillator-related and Kepler-related systems
• Superintegrability on the 3-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the Sphere $S^3$ and on the Hyperbolic space $H^3$
• Algebraic structures and deformed Schrödinger equations from groups entropies