Factorization Method and Special Orthogonal Functions

Abstract

We present a general construction for ladder operators for the special orthogonal functions based on Nikiforov-Uvarov mathematical formalism. A list of creation and annihilation operators are provided for the well known special functions. Furthermore, we establish the dynamic group associated with these operators.

An Algebraic Approach to the Kemmer Equation for Dirac Oscillator

“…By using Nikiforov-Uvarov mathematical method [12][13][14][15] one can easily obtain the exact solution of (9) as…”

“…where, we have used the normalization constant N n in relation (13). By comparing this relation with (19) we getL…”

“…which can be recognized as commutation relation of the generators of a non-compact Lie algebra su (1,1). The corresponding Casimir operator is defined bŷ…”

“…In recent years, the algebraic methods have been widely used in various fields of physics [1][2][3][4]. These methods play important roles in the study of a given quantum system with exact solutions.…”

“…In addition, in this approach the hidden symmetry of the system may be discovered by constructing a suitable Lie algebra, which can be realized by the ladder operators [5]. It is well known that these operators can be established from the factorization method [1]. Factorization method is a basic technique that reduces the dynamic equation of a given system into a simple one which is easier to handle.…”