Configuration-Space Approach to the Four-Particle Problem

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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.