Response Equations for Quantum-Classical Systems

DERIVATION OF RESPONSE EQUATIONS FOR QUANTUM-CLASSICAL SYSTEMS [Pg.369]

We will in this section consider the mathematical structure for computational procedures when calculating molecular properties of a quantum mechanical subsystem coupled to a classical subsystem. Molecular properties of the quantum subsystem are obtained when considering the interactions between the externally applied time-dependent electromagnetic field and the molecular subsystem in contact with a structured environment such as an aerosol particle. Therefore, we need to study the time evolution of the expectation value of an operator A and we express that as [Pg.369]

Our starting point is the following, we have a wave function and an energy functional that has been optimized in the presence of the structured environment and therefore, we have the physically correct state of the quantum mechanical subsystem coupled to the structured environment. [Pg.370]

Our wish to study how the quantum mechanical subsystem evolves in time requires that we select appropriate operators, that will provide time propagation of the wave functions. These unitary transformation operators are [Pg.370]

Furthermore, we define a set of operators, T, that will enable us to follow the evolution of fhe quantum subsystem [Pg.371]