Principal-axis hyperspherical description ofN-particle systems: Quantum-mechanical treatment

Principal-axis hyperspherical coordinates (made up of one hyperradius and 3N-7 angles as internal coordinates) and three Euler angles as external (rotational) coordinates [X. Chapuisat and A. Nauts, Phys. Rev. A 44, 1328 (1991)], are used to describe an N-particle system. The exact quantum-mechanical Hamiltonian of the system in terms of these coordinates is established and is very simple. Generalized angular-momentum vector operators, which allow the generation of a profitable standard representation for the angular part of the problem, are introduced. The corresponding matrix representation of the Hamiltonian operator is built.