Browsing by Subject "superintegrability"

Now showing items 1-7 of 7

  • Hamilton-Jacobi Theory and Superintegrable Systems

    Armstrong, Craig Keith (The University of Waikato, 2007)
    Hamilton-Jacobi theory provides a powerful method for extracting the equations of motion out of some given systems in classical mechanics. On occasion it allows some systems to be solved by the method of separation of ...
  • Models for quadratic algebras associated with second order superintegrable systems in 2D

    Kalnins, Ernie G.; Miller, W., Jr.; Post, Sarah (SIGMA, 2008-01)
    There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite ...
  • A recurrence relation approach to higher order quantum superintegrability

    Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr. (2011)
    We develop our method to prove quantum superintegrability of an integrable 2D system, based on recurrence relations obeyed by the eigenfunctions of the system with respect to separable coordinates. We show that the method ...
  • Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems

    Kalnins, Ernie G.; Miller, W., Jr. (the Department of Applied Research, Institute of Mathematics of National Academy of Sciences of Ukraine, 2012)
    The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order ...
  • Structure theory for second order 2D superintegrable systems with 1-parameter potentials

    Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr.; Post, Sarah (2009)
    The structure theory for the quadratic algebra generated by first and second order constants of the motion for 2D second order superintegrable systems with nondegenerate (3-parameter) and or 2-parameter potentials is well ...
  • Tools for verifying classical and quantum superintegrability

    Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr. (Kiev, 2010)
    Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n−1 symmetries polynomial in the canonical momenta, ...
  • Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere

    Kalnins, Ernie G.; Miller, W., Jr.; Post, Sarah (2011)
    We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 ...