It is shown that the one-dimensional Dunkl-Dirac equation can be decoupled into
Schrödinger form, provided parity requirements on both solution and potential are met. We …

We devise a method for constructing solvable cases of generalized linear Dunkl-
Schrödinger equations by means of suitable point transformations. The quantum …

We construct a momentum operator within the Wigner–Heisenberg algebra picture by
means of a generalized derivative, a particular case of which is the Dunkl operator. The …

We consider the quantum mechanics of Calogero models in an oscillator or Coulomb
potential on the N-dimensional sphere. Their Hamiltonians are obtained by an appropriate …

We introduce the Dunkl version of the Laplace–Runge–Lenz vector associated with a finite
Coxeter group W acting geometrically in RN and with a multiplicity function g. This vector …

We propose the superintegrable generalization of Smorodinsky–Winternitz system on the N-
dimensional complex Euclidian space which is specified by the presence of constant …

We propose a unified description for the constants of motion for superintegrable
deformations of the oscillator and Coulomb systems on N-dimensional Euclidean space …

We give a solution to the long-standing problem of constructing the generators of hidden
symmetries of the quantum Higgs oscillator, a particle on a d-sphere moving in a central …

We propose a new superintegrable mechanical system on the complex projective space CP
N involving a potential term together with coupling to a constant magnetic fields. This system …

We use a symmetrized Hamiltonian containing Dunkl operators to generate a Dunkl–
Schrödinger equation with position-dependent mass. Our equation is shown to admit …