Infeld-Hull Factorization Research Articles

Creation and annihilation operators, symmetry and supersymmetry of the 3D isotropic harmonic oscillator

We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld–Hull factorization method.

Raising and lowering operators, factorization and differential/difference operators of hypergeometric type

Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type.

An algebraic form of the factorization method

The Infeld-Hull factorization method is recast in more general algebraic form which may be looked at as the most natural extension of the oscillator algebra. Nonrelativistic and relativistic hydrogen problems appear simpler and perfectly analogous, whereby the factors in both cases are directly related to the characteristic hidden symmetries. Close connections to nonlinear problems and more general algebraic properties yield relations to recent developments.

Infeld-Hull factorization and the simplified solution of the Dirac-Coulomb equation.

It is pointed out that the approach used by Su to obtain the simplified solution to the Dirac-Coulomb equation can be interpreted in the light of the Infeld-Hull factorization method. According to this method the first-order Dirac-Coulomb equation, after the transformation S-italic, necessarily implies two second-order ''Schroedinger-type'' equations, whose solutions are the upper and lower simplified solutions of the Dirac-Coulomb equation. It is also interesting to note that the ''recurrence relation'' between the upper and lower solutions, first obtained by Biedenharn, is exactly the Dirac-Coulomb equation itself, after the transformation S-italic.

Construction of dynamical symmetry group of the relativistic harmonic oscillator by the Infeld-Hull factorization method

Construction of dynamical symmetry group of the relativistic harmonic oscillator by the Infeld-Hull factorization method

Infeld–Hull factorization, Galois–Picard–Vessiot theory for differential operators

The Infeld–Hull theory of factorization of second order differential operators is related, on the one hand, to the classical Picard–Vessiot theory and, on the other hand, to work by the author, Gel’fand, and Kirillov on Lie algebras contained in the field of fractions or algebraic extensions of the enveloping associative algebra of a Lie algebra.

New types of factorizable equations

AbstractBy a generalization of the Infeld-Hull Factorization Kernels we find it possible to factorize a wide family of second-order ordinary differential equations at specified points of their spectrum.

Self-Adjoint Ladder Operators (I)

The theory of self-adjoint ladder operators is outlined, a comparison being made with the more usual type of ladder operator. It is shown how the method applies to the $n$-dimensional orbital angular momentum problem, for which it is found that the ladder operator may be expressed as a linear combination of the components of angular momentum, the expansion coefficients being the elements of a generalized spin algebra. Its relationship to the Infeld-Hull factorization method is discussed, the factorization appearing as part of a more general scheme. The physical significance of the ladder operators is emphasized through their application to the relativistic quantum theory of Dirac.