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 …
Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality
O Mustafa, Z Algadhi - The European Physical Journal Plus, 2019 - epjplus.epj.org
The classical and quantum-mechanical correspondence for constant mass settings is used,
along with some point canonical transformation, to find the position-dependent mass (PDM) …
along with some point canonical transformation, to find the position-dependent mass (PDM) …
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 …
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 …
General Nth-order superintegrable systems separating in polar coordinates
AM Escobar-Ruiz, P Winternitz… - Journal of Physics A …, 2018 - iopscience.iop.org
The general description of superintegrable systems with one polynomial integral of order N
in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane …
in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane …
The singular and the 2: 1 anisotropic Dunkl oscillators in the plane
Two Dunkl oscillator models are considered: one singular and the other with a 2: 1
frequency ratio. These models are defined by Hamiltonians which include the reflection …
frequency ratio. These models are defined by Hamiltonians which include the reflection …
n-dimensional PDM non-linear oscillators: linearizability and Euler–Lagrange or Newtonian invariance
O Mustafa - Physica Scripta, 2020 - iopscience.iop.org
We argue that, under multidimensional position-dependent mass (PDM) settings, the Euler–
Lagrange textbook invariance falls short and turned out to be vividly incomplete and/or …
Lagrange textbook invariance falls short and turned out to be vividly incomplete and/or …
General Nth order integrals of motion in the Euclidean plane
S Post, P Winternitz - Journal of Physics A: Mathematical and …, 2015 - iopscience.iop.org
The general form of an integral of motion that is a polynomial of order N in the momenta is
presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and …
presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and …