Spheroconal harmonic angular momentum

ON DEVELOPING THE THEORY OF ANGULAR MOMENTUM IN BASES OF LAhAi SPHEROCONAL HARMONICS... 

In Section 4.1, the identification of complefe radial and angular momentum raising and lowering operators for fhe familiar spherical harmonics is presented in our own version, as a point of reference for some extensions in Section 4.2 for fhe spheroconal harmonics. The resulfs in Section 4.1 have been known in the literature [44, 46], but here the interest is in their adaptation and extension to eigenfunctions of P and Lf, and and H. ... 

The method and results of this section also illuminate some of our works on rotations of asymmetric molecules, the hydrogen atom and any central potential in the direction of developing the theory of angular momentum in the Lam6 spheroconal harmonic bases, as discussed in the following sections. 

Angular momentum transformations of Lam6 spheroconal harmonic polynomials... 

The familiar theory of angular momentum, based on spherical harmonics, eigenfunctions of and operators of angular momentum, also uses the ladder operators L , which for a given value of i connect all the 2 - -1 successive states m) with m = —I, -I + 1,..., —1,0,1,..., -1,1. Section 4.2.1 illustrates the counterpart for the spheroconal harmonics or the spherical harmonics with well-defined parities under the application of the operators... 

The topics of this chapter, listed in the Contents and outlined in the Introduction, discuss the rotations of asymmetric molecules and the hydrogen atom in their natural free configurations as reviewed in Section 2 changes in the properties of the same systems in configurations of confinement by elliptical cones are reported, including new results for asymmetric molecules, in Section 3 and some advances in developing the theory of angular momentum in spheroconal harmonic bases, as well as some possible routes under exploration are presented in Section 4. 

Ghapter 4 presents a review of fhe exacf formulafions and evaluafions for the rotations of free asymmefric molecules and for treafment of fhe sysfems when confined by boundary condifions including elliptical cones. In addition, some tools and advances in development in the theory of angular momentum in bases of spheroconal harmonics are discussed. 

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