Related papers: Hyperspherical harmonics with arbitrary arguments

Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…

We give an algebraic derivation of the eigenvalues of energy of a quantum harmonic oscillator on the surface of constant curvature, i.e. on the sphere or on the hyperbolic plane. We use the method proposed by Daskaloyannis for fixing the…

We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for…

We introduce a number of tools for finding and studying \emph{hierarchically hyperbolic spaces (HHS)}, a rich class of spaces including mapping class groups of surfaces, Teichm\"{u}ller space with either the Teichm\"{u}ller or…

Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…

We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…

For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of the representations of G on spaces of regular sections of homogeneous…

The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific…

For a particular case of three-body scattering in two dimensions, and matching analytical expressions at a transition point, we obtain accurate solutions for the hyperspherical adiabatic basis and potential. We find analytical expressions…

We define hyperbolic Heron triangles (hyperbolic triangles with "rational" side-lengths and area) and parametrize them in two ways as rational points of certain elliptic curves. We show that there are infinitely many hyperbolic Heron…

Using the characterizations in terms of various differential operators including partial, normal, and tangential derivatives, we extend the family of Bergman spaces of $\mathcal H$-harmonic functions on the real hyperbolic ball from…

A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…

This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory. We discuss both continuous and discrete orthogonal…

We consider the 4-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative…

Using a formulation of quantum mechanics based on orthogonal polynomials in the energy and physical parameters, we present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy…

A family of harmonic superspaces associated with four-dimensional spacetime is described. Some applications to supersymmetric field theories, including supergravity, are given.

Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle system characterised by a generic such Hamiltonian is worked…

It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…