Перегляд за автором "Miller Jr., W."

Сортувати за: Порядок: Результатів:

  • A Recurrence Relation Approach to Higher Order Quantum Superintegrability 
    Kalnins, E.G.; Kress, J.M.; Miller Jr., W. (Symmetry, Integrability and Geometry: Methods and Applications, 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 ...
  • Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras 
    Escobar Ruiz, M.A.; Kalnins, E.G.; Miller Jr., W.; Subag, E. (Symmetry, Integrability and Geometry: Methods and Applications, 2017)
    Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical ...
  • Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials 
    Kalnins, E.G.; Miller Jr., W.; Post, S. (Symmetry, Integrability and Geometry: Methods and Applications, 2013)
    We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method ...
  • Contractions of Degenerate Quadratic Algebras, Abstract and Geometric 
    Escobar Ruiz, M.A.; Subag, E.; Miller Jr., W. (Symmetry, Integrability and Geometry: Methods and Applications, 2017)
    Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical ...
  • Examples of Complete Solvability of 2D Classical Superintegrable Systems 
    Chen, Y.; Kalnins, E.G.; Li, Q.; Miller Jr., W. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    Classical (maximal) superintegrable systems in n dimensions are Hamiltonian systems with 2n−1 independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be ...
  • Models for Quadratic Algebras Associated with Second Order Superintegrable Systems in 2D 
    Kalnins, E.G.; Post, S.; Miller Jr., W. (Symmetry, Integrability and Geometry: Methods and Applications, 2008)
    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 ...
  • Structure Relations and Darboux Contractions for 2D 2nd Order Superintegrable Systems 
    Heinonen, R.; Kalnins, E.G.; Miller Jr., W.; Subag, E. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
    Two-dimensional quadratic algebras are generalizations of Lie algebras that include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly ...
  • Structure Theory for Extended Kepler-Coulomb 3D Classical Superintegrable Systems 
    Kalnins, E.G.; Miller Jr., W. (Symmetry, Integrability and Geometry: Methods and Applications, 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, E.G.; Kress, J.M.; Post, S.; Miller Jr., W. (Symmetry, Integrability and Geometry: Methods and Applications, 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 ...
  • Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere 
    Kalnins, E.G.; Miller Jr., W.; Post, S. (Symmetry, Integrability and Geometry: Methods and Applications, 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 ...