  A new general formalism for determining the electric multipole
polarizabilities of quantum (atomic and nuclear) bound systems based on the use
of the transition matrix in momentum space has been developed. As distinct from
the conventional approach with the application of the spectral expansion of the
total Green's function, our approach does not require preliminary determination
of the entire unperturbated spectrum; instead, it makes possible to calculate
the polarizability of a few-body bound complex directly based on solving
integral equations for the wave function of the ground bound state and the
transition matrix at negative energy, both of them being real functions of
momenta. A formula for the multipole polarizabilities of a two-body bound
complex formed by a central interaction potential has been derived and studied.
To test, the developed $T$-matrix formalism has been applied to the calculation
of the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.
