Quantum description of rigidly or adiabatically constrained four-particle systems and supersymmetry

A general formalism for the quantum description of many-body systems is developed, using the principal-axis hyperspherical parametrization of coordinates. This formalism is applied to four-particle systems for which the exact kinetic energy operator is derived using a model constraints and dynamical constraints. Then, using the supersymmetry and shape invariance approach, we obtained in a closed form the eigenvalues and eigenfunctions of a wide class of noncentral potentials for the adiabatically constrained four-particle systems. (C) 1999 American Institute of Physics. [S0022-2488(99)00112-7].