Grand angular momentum

Here, Vc is the sum of all the two-body interactions and A( 2C) is the angular momentum operator suitable for the five-dimensional angular space. The latter is referred to as the grand angular momentum operator. It introduces the centrifugal potential for the motion in p. It takes an explicit form... 

Eigenfunctions of the grand-angular momentum are called hyperspherical harmonics. They form a complete set of eigenfunctions in i -space and could be used to represent the variation of p O) at fixed p. However, too many of them are in general needed to represent the wavefunction accurately, especially at large p. 

F = grand total angular momentum including electron and nuclear spin R = internuclear distance , 9, x = Euler angles... 

In 11.3.4 we mentioned that the electrons in the atomic shell have Russell-Saunders coupling (11.18), J = L + S, where J is referred to as the internal quantum number. The magnetic field created by the electrons interacts with that caused by the nuclear spin to yield the grand atomic angular momentum vector... 

The grand canonical angular momentum operator A is defined as... 

Harmonics of given total (ordinary) angular momentum / = / + / > (not to be confused with the grand orbital momentum L) are constructed by Clebsch-Gordan coupling of the HH (5.10). One should further restrict the expansion (5.6) to these HH having the desired permutation properties. 

At the end of the nineteenth century classical physics assumed it had achieved a grand synthesis. The universe was thought of as comprising either matter or radiation as illustrated schematically in Fig. 2.1. The former consisted of point particles which were characterized by their energy E and momentum p and which behaved subject to Newton s laws of motion. The latter consisted of electromagnetic waves which were characterized by their angular frequency and wave vector and which satisfied Maxwell s recently discovered equations, ( = 2nv and — 2njX where v and X are the vibrational frequency... 

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