Sevaration of “normal” and “superfluid” mctions in the Schrödinger equation by means of the method of displacements and collective variables

By the application of a displacement transformation, the wave function of a system of interacting bosons is represented by the product of the ground-state wave function and a function that describes the presence of excitations in the system. The equations obtained for these functions are solved in the representation of collective variables by a special method of perturbation theory that does not contain divergences. An investigation is made of the resulting expressions for the wave functions, ground-state energy, energy spectrum, and damping of collective excitations.