We address the problem of obtaining the exact reduced dynamics of the
spin-half (qubit) immersed within the bosonic bath (enviroment). An exact
solution of the Schrodinger equation with the paradigmatic spin-boson
Hamiltonian is obtained. We believe that this result is a major step ahead and
may ultimately contribute to the complete resolution of the problem in
question. We also construct the constant of motion for the spin-boson system.
In contrast to the standard techniques available within the framework of the
open quantum systems theory, our analysis is based on the theory of block
operator matrices.Comment: 9 pages, LaTeX, to appear in Journal of Physics A: Mathematical and
Theoretica