The quantum dynamics of three particles in hyperspherical coordinates

A derivation of the quantum mechanical wave equation for the three body problem expressed in hyperspherical coordinates is presented. The coordinates, due to Smith and Whitten and later modified by Johnson [B. R. Johnson, J. Chem. Phys. 73, 5051 (1980)], are used in this study. The analysis is presented from a point of view that emphasizes the role of the three-dimensional configuration space that is associated with these coordinates. Three types of motion are analyzed: full three dimensional; motion restricted to a plane surface; and zero angular momentum motion.