This thesis is primarily concerned with the description and development of the Quantum Classical Moment ( QCM) approach introduced
by Burghardt and Parlant. This scheme combines the quantum hydrodynamic and classical Liouvillian representations by generating
partial hydrodynamic moments. The time evolution of the partial
moments are governed by a hierarchy of coupled equations. For
pure quantum states, the hierarchy terminates at the first order.
The application of the QCM approach for pure states subject to anharmonic potentials ( double well and Eckart barrier) coupled to a
classical harmonic mode is demonstrated in Chapter 4. However, in
the hydrodynamic formulation of mixed quantum states, no simple
closure to the hierarchy exists.
Chapter 5 develops a closure scheme that uses information embedded
in the known lower order moments to expand the underlying Wigner
phase space distribution function in a Gauss-Hermite orthonormal
basis. The application of the closure scheme is demonstrated for
both dissipative and nondissipative dynamics of various potentials.
The thesis concludes with a presentation of the extended molecular hydrodynamic approach to describe non-adiabatic salvation phenomena. A mixed quantum-classical description of the system is
derived where a classical solvent interacts with a quantum two level
solute. A comparison of the dynamics of the hydrodynamic fields
obtained from the extended molecular hydrodynamic approach is
made with the phase space approach. The differences observed are
attributable to the moment hierarchy approximation made in the
molecular hydrodynamic scheme.