相关论文: The factorization of the hypergeometric equation

We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…

A generalized version of the creation and annihilation operators is constructed and the factorization of the Schr\"odinger equation is investigated. It is shown that the generalized version of factorization operators yield a factorization…

Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…

In 1960 Schwinger [J. Schwinger, Proc.Natl.Acad.Sci. 46 (1960) 570- 579] proposed the algorithm for factorization of unitary operators in the finite M dimensional Hilbert space according to a coprime decomposition of M. Using a special…

In this article we give an example of a matrix version of the famous congruence for hypergeometric functions found by Dwork in 'p-adic cycles'.

A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…

Original English Summary. - A systematic method of constructing potentials, for which the one-variable Schroedinger equation can be solved in terms of the hypergeometric (HGM) function, is presented. All the potentials, obtained by…

In this paper, we study some extended hypergeometric functions from matrix point of view. We have given the integral representations of these matrix functions. Finally, we obtain some generating function relations using fractional…

This paper addresses a general method of polynomial transformation of hypergeometric equations. Examples of some classical special equations of mathematical physics are generated. Heun's equation and exceptional Jacobi polynomials are also…

We propose a geometric explanation for the observation that generic quadratic polynomials over split quaternions may have up to six different factorizations while generic polynomials over Hamiltonian quaternions only have two. Split…

This paper is devoted to a factorization of the higher dimensional Schrodinger operator in the framework of Clifford analysis.

This is a brief review of the Schrodinger's factorization method and its relations to supersymmetric quantum mechanics and its nonlinear (parastatistical, etc) modifications, self-similar infinite soliton potentials, quantum algebras,…

In this note we solve a problem about the rational representablility of hupergeometric terms which represent hypergeometric sums. This problem was proposed by Koornwinder in [4].

We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…

We construct a class of representations of the quadratic R-matrix algebra, given by the reflection equation with the spectral parameter, in terms of certain ordinary difference operators. These operators turn out to act as parameter…

The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general $_2\psi_2$ series is examined in detail. Connections are found with the theory of basic hypergeometric series on…

We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing…

The scattering matrix for the full-line matrix Schr\"odinger equation is analyzed when the corresponding matrix-valued potential is selfadjoint, integrable, and has a finite first moment. The matrix-valued potential is decomposed into a…

We obtain the double factorization of braided bialgebras or braided Hopf algebras, give relation among integrals and semisimplicity of braided Hopf algebra and its factors.

We generalize Schroedinger's factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach, is the fact that the Hamiltonian is represented…