Description of the spectrum of the energy operator of quantum-mechanical systems that is invariant with respect to permutations of identical particles

Methods are developed for investigating the spectra of the energy operators of many-particle quantum-mechanical systems that are invariant with respect to permutations of identical particles. The configuration space of the system is decomposed into a sum of subspaces corresponding to the motion of the system with respect to the center of mass and the motion of the center of mass itself. The energy operator of the system is decomposed accordingly. The operator of the energy of the relative motion of the system obtained in this manner is studied on the hyperplane of the motion of the system relative to the center of mass. This ensures the invariance of the methods developed.