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

The invariant separation of the motion of the center of mass clarifies the physical meaning of the special cases when the system decomposes into two identical subsystems. The energy theorem of Sec. 7 is contained in a more complicated form in [3]. One can show that both these theorems are equivalent. The interaction potentials Vij(ri-r j) , considered in this investigation include, in particular~ all Coulomb potentials and, quite generally, all pair interactions encountered in physics. *This paper is a further development of an unpublished paper of A.T. Gavrilin and I.M. Sigal completed under the direction of A.G. Sigalov at the Gor'kii State University in 1968. Deceased.