Classical and quantum superintegrability with applications
W Miller, S Post, P Winternitz - Journal of Physics A: Mathematical …, 2013 - iopscience.iop.org
A superintegrable system is, roughly speaking, a system that allows more integrals of motion
than degrees of freedom. This review is devoted to finite dimensional classical and quantum …
than degrees of freedom. This review is devoted to finite dimensional classical and quantum …
Nonlinear supersymmetric quantum mechanics: concepts and realizations
The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum
mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is …
mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is …
The Dunkl oscillator in the plane: I. Superintegrability, separated wavefunctions and overlap coefficients
The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a
Hamiltonian constructed from the combination of two independent parabosonic oscillators …
Hamiltonian constructed from the combination of two independent parabosonic oscillators …
[BOOK][B] Continuous symmetries and integrability of discrete equations
D Levi, P Winternitz, RI Yamilov - 2023 - books.google.com
This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …
symmetries and integrability techniques to the case of equations defined on the lattice. This …
Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials
EG Kalnins, W Miller Jr, S Post - SIGMA. Symmetry, Integrability and …, 2013 - emis.de
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 …
cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our …
Periodic orbits for an infinite family of classical superintegrable systems
F Tremblay, AV Turbiner… - Journal of Physics A …, 2009 - iopscience.iop.org
We show that all bounded trajectories in the two-dimensional classical system with the
potential are closed for all integer and rational values of k. The period is and does not …
potential are closed for all integer and rational values of k. The period is and does not …
An infinite family of superintegrable deformations of the Coulomb potential
S Post, P Winternitz - Journal of Physics A: Mathematical and …, 2010 - iopscience.iop.org
We introduce a new family of Hamiltonians with a deformed Kepler–Coulomb potential
dependent on an indexing parameter k. We show that this family is superintegrable for all …
dependent on an indexing parameter k. We show that this family is superintegrable for all …
Algebraic (super-) integrability from commutants of subalgebras in universal envelo** algebras
R Campoamor-Stursberg, D Latini… - Journal of Physics A …, 2023 - iopscience.iop.org
Starting from a purely algebraic procedure based on the commutant of a subalgebra in the
universal envelo** algebra of a given Lie algebra, the notion of algebraic Hamiltonians …
universal envelo** algebra of a given Lie algebra, the notion of algebraic Hamiltonians …
Fourth order superintegrable systems separating in polar coordinates. I. Exotic potentials
We present all real quantum mechanical potentials in a two-dimensional Euclidean space
that have the following properties: 1. They allow separation of variables of the Schrödinger …
that have the following properties: 1. They allow separation of variables of the Schrödinger …
Families of superintegrable Hamiltonians constructed from exceptional polynomials
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave
functions are given in terms of Laguerre and exceptional Jacobi polynomials. The …
functions are given in terms of Laguerre and exceptional Jacobi polynomials. The …