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6 papers · 2 filters
Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems
Ian Marquette
There exist a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude (SVPEM) and the Schrodinger equation. We obtain the rel…
An infinite family of superintegrable systems from higher order ladder operators and supersymmetry
Ian Marquette
We will discuss how we can obtain new quantum superintegrable Hamiltonians allowing the separation of variables in Cartesian coordinates with higher order integrals of motion from…
Affine Constellations Without Mutually Unbiased Counterparts
Stefan Weigert, Thomas Durt
It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine cons…
Quantum Fourier transform, Heisenberg groups and quasiprobability distributions
Manas K. Patra, Samuel L. Braunstein
This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for cont…
Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras
Ian Marquette
We present the quadratic algebra of the generalized MICZ-Kepler system in three-dimensional Euclidean space and its dual the four dimensional singular oscillator in four-di…
Construction of classical superintegrable systems with higher order integrals of motion from ladder operators
Ian Marquette
We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher…