  There is developed a current algebra representation scheme for reconstructing
algebraically factorized quantum Hamiltonian and symmetry operators in the Fock
type space and its application to quantum Hamiltonian and symmetry operators in
case of quantum integrable spatially many- and one-dimensional dynamical
systems. As examples, we have studied in detail the factorized structure of
Hamiltonian operators, describing such quantum integrable spatially many- and
one-dimensional models as generalized oscillatory, Calogero-Sutherland, Coulomb
type and nonlinear Schr\"{o}dinger dynamical systems of spinless
bose-particles.
