  It is shown that any two Hamiltonians H(t) and H'(t) of N dimensional quantum
systems can be related by means of time-dependent canonical transformations
(CT). The dynamical symmetry group of system with Hamiltonian H(t) coincides
with the invariance group of H(t). Quadratic Hamiltonians can be diagonalized
by means of linear time-dependent CT. The diagonalization can be explicitly
carried out in the case of stationary and some nonstationary quadratic H.
Linear CT can diagonalize the uncertainty matrix \sigma(\rho) for canonical
variables p_k, q_j in any state \rho, i.e., \sigma(\rho) is symplectically
congruent to a diagonal uncertainty matrix. For multimode squeezed canonical
coherent states (CCS) and squeezed Fock states with equal photon numbers in
each mode \sigma is symplectic itself. It is proved that the multimode
Robertson uncertainty relation is minimized only in squeezed CCS.
