Related papers: Runge-Lenz vector in Calogero-Coulomb problem
Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
The problem of the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on phase space. The original work of Zaslovskii {\it et al} showed that the resulting evolution contains a…
We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…
We study deformations of the quantum conformal mechanics of De Alfaro-Fubini-Furlan with rational additional potential term generated by applying the generalized Darboux-Crum-Krein-Adler transformations to the quantum harmonic oscillator…
We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$…
We generalize the Donsker-Varadhan minimax formula for the principal eigenvalue of a uniformly elliptic operator in nondivergence form to the first principal half-eigenvalue of a fully nonlinear operator which is concave (or convex) and…
The electric interaction between two nearby evolving electrons triggers the correlation between their waves and governs the operation of logical devices called Coulomb entanglers. Of technological interest in the presence of magnetic fields…
The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in which the momentum generators no longer commute, but satisfy $[P_\mu,P_\nu]=Z_{\mu\nu}$. The charges $Z_{\mu\nu}$ commute with the momenta, and transform…
We investigate common algebraic structure for the rational and trigonometric Calogero-Sutherland models by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides…
We establish a direct link between Dunkl operators and quantum Lax matrices $\mathcal L$ for the Calogero--Moser systems associated to an arbitrary Weyl group $W$ (or an arbitrary finite reflection group in the rational case). This…
The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…
We formulate a general principle that supplants a Boolean \sigma-algebra of intrinsic properties of a classical system by a \sigma-complex (a union of \sigma-algebras) of extrinsic properties of a quantum system that are elicited by…
The Dunkl total angular momentum algebra (TAMA) is realised as the dual partner of the orthosymplectic Lie superalgebra containing the Dunkl deformation of the Dirac operator. In this paper, we consider the case when the reflection group…
The dynamics of a set of identical spins interacting with another one through a time-dependent coupling gives rise to a gyroscopic equation with a variable Larmor frequency and, more importantly, with an operator playing the role a Larmor…
The work analyzes the theory of Dunkl operator as a moment differential operator. This last operator generalizes the first one whenever the sequence of moments satisfies appropriate classical properties, classically considered in the…
The Kustaanheimo-Stiefel (KS) transformation maps the non-linear and singular equations of motion of the three-dimensional Kepler problem to the linear and regular equations of a four-dimensional harmonic oscillator. It is used extensively…
Recent results are surveyed pertaining to the complete integrability of some novel n-particle models in dimension one. These models generalize the Calogero-Moser systems related to classical root systems. Quantization leads to difference…
We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…
Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper…