  The quantum dynamics of a simplest dissipative system, a particle moving in a
constant external field , is exactly studied by taking into account its
interaction with a bath of Ohmic spectral density. We apply the main idea and
methods developed in our recent work [1] to quantum dissipative system with
constant external field. Quantizing the dissipative system we obtain the simple
and exact solutions for the coordinate operator of the system in Heisenberg
picture and the wave function of the composite system of system and bath in
Schroedinger picture. An effective Hamiltonian for the dissipative system is
explicitly derived from these solutions with Heisenberg picture method and
thereby the meaning of the wavefunction governed by it is clarified by
analyzing the effect of the Brownian motion. Especially, the general effective
Hamiltonian for the case with arbitrary potential is directly derived with this
method for the case when the Brownian motion can be ignored. Using this
effective Hamiltonian, we show an interesting fact that the dissipation
suppresses the wave packet spreading.
