APPROACH OF THE AZIMUTHAL AND MAGNETIC QUANTUM NUMBERS l AND m TO REPRESENTATION OF A CUBIC DEFORMATION OF su(2) ALGEBRA

Abstract

It is shown that the space of spherical harmonics [Formula: see text] whose 2l - m = p - 1 is given, represent irreducibly a cubic deformation of su(2) algebra, the so-called su Φp(2), with deformation function as [Formula: see text]. The irreducible representation spaces are classified in three different bunches, depending on one of values 3k - 2, 3k - 1 and 3k, with k as a positive integer, to be chosen for p. So, three different methods for generating the spectrum of spherical harmonics are presented by using the cubic deformation of su(2). Moreover, it is shown that p plays the role of deformation parameter.