Generalized Radial Equations in a Quantum N-Body Problem

Abstract

We demonstrate how to separate the rotational degrees of freedom in a quantum N-body problem completely from the internal ones. It is shown that any common eigenfunction of the total orbital angular momentum ($\ell$) and the parity in the system can be expanded with respect to $(2\ell+1)$ base-functions, where the coefficients are the functions of the internal variables. We establish explicitly the equations for those functions, called the generalized radial equations, which are $(2\ell+1)$ coupled partial differential equations containing only $(3N-6)$ internal variables.