Variational principles and the virial theorem in quantum scattering theory

Problems concerning some functionals of quantum scattering theory in three-dimensional space are studied. Variation principles for these functionals are formulated. The virial theorem for the continuous spectrum is derived with the aid of one of these variation principles. This theorem makes it possible to obtain a new representation for the spectral shift function. On the basis of this representation the new expression for the second group integral is found.