The Separation of the Rotational Coordinates from the N-Particle Schroedinger Equation

Abstract

By group theoretical arguments, it can be shown that a wave function, ψμL, for a system of N particles corresponding to a total angular momentum quantum number, L, and a quantum number, μ, referring to the z component of angular momentum may be written as a sum of terms: ψμL=Σs DL(R)μs*χsL.The DL(R)μs are the representation coefficients for the Lth irreducible representation of the three-dimensional rotation group, and are functions of the three coordinates specifying the orientation of the system of particles in space. The χμL are functions of the 3N−6 coordinates specifying the relative configuration of the N-particle system. The set of coupled differential equations for the functions, χμL, is obtained explicitly. The special case of the three-particle system is discussed in detail. The present treatment is more directly usable than the previous discussions since the basic equations do not involve implicit relationships between the variables.