The three-body problem in the path integral formalism (Q1877779)

The three-body problem is explored in the framework of Feynman path integral method. Three particles of equal masses subjected to the one-dimensional Calogero potential are considered (as well as some generalizations of this situation). The corresponding propagator is calculated in the phase-space Feynman formalism. The energy spectrum is determined along with the corresponding wave functions. In case if some constraints are introduced, the problem is reduced to a particle constrained to move in a sector of angle \(\alpha\).