Quantum description of five-particle systems in principal-axis hyperspherical coordinates

To describe a 5-particle system, ʹprincipal-axis hypersphericalʹ coordinates (made up of one hyperradius and eight angles as internal coordinates) and three Euler angles as external (rotational) coordinates are used. A mathematical procedure to derive, in a systematic manner, the exact quantum mechanical Hamiltonian of the system in terms of these coordinates is presented. A generalized angular momentum vector operator, which allows the generation of a profitable standard representation for the angular part of the problem, is introduced.