We discuss the physical problem of a molecule interacting with an electromagnetic field pulse and model the problem using a time-dependent perturbation of the Born-Oppenheimer approximation to the Schrodinger equation. Using previous results that develop asymptotic series solutions in the Born-Oppenheimer parameter ε, we derive a formal Dyson series expansion in the perturbation parameter μ, which is proportional to the electromagnetic field strength. We then prove that this series is asymptotically accurate in both parameters, provided that the Hamiltonian for the electrons has purely discrete spectrum. Under more general hypotheses, we show that the series is accurate to first order in μ, and that it is accurate to one higher order if we place conditions on the abruptness of the EM pulse. We also show how this series development provides a justification for the Franck-Condon factors in the case of a diatomic molecule. / Ph. D.

The aim of this work is to investigate projection operator method of deriva- tion of equations of motion for reduced density matrix and apply it to a model open quantum system. We gradually pass from quantum mechanical model of a molecule with one vibrational degree of freedom to an example of open quantum system relevant in the theory of nonlinear spectroscopy. In the thesis we present results of numerical simulations of the time evolution of the open quantum system performed with a program written for this purpose. We are specially concerned with simulations of the solution of the time-convolutionless generalized master equation up to the a second order of the perturbation expan- sion, and we show that under certain conditions it provides an exact solution of the problem. The text also contains derivation of the recurrence relations for the Franck-Condon factors for the most general case of two quantum harmonic oscillators in one space dimension, i. e. transformation matrix between two bases of the L2 (R) space determined by the solutions of the time-independent Schrödinger equation appropriate for these oscillators. 1