Configuration-Space Approach to the Four-Particle Problem

Abstract

The configuration‐space approach to the three‐particle problem is generalized to the case of four particles. Special coordinates are defined which have simple symmetry properties with respect to the exchange of identical particles. The construction of a suitable orthogonal system is discussed. Some of these functions are given explicitly. It is pointed out that the use of this orthogonal system leads to a considerable simplification for a large number of four‐particle problems, namely, the approximate reduction of the Schrödinger equation to a finite system of coupled differential equations for functions that depend on one variable only.