Quantum Dynamics of Molecular Systems and Guided Matter Waves

Sammanfattning: Quantum dynamics is the study of time-dependent phenomena in fundamental processes of atomic and molecular systems. This thesis focuses on systems where nature reveals its quantum aspect; e.g. in vibrational resonance structures, in wave packet revivals and in matter wave interferometry. Grid based numerical methods for solving the time-dependent Schrödinger equation are implemented for simulating time resolved molecular vibrations and to compute photo-electron spectra, without the necessity of diagonalizing a large matrix to find eigenvalues and eigenvectors.Pump-probe femtosecond laser spectroscopy on the sodium potassium molecule, showing a vibrational period of 450 fs, is theoretically simulated. We find agreement with experiment by inclusion of the finite length laser pulse and finite temperature effects.Complicated resonance structures observed experimentally in photo-electron spectra of hydrogen- and deuterium chloride is analyzed by a numerical computation of the spectra. The dramatic difference in the two spectra arises from non-adiabatic interactions, i.e. the interplay between nuclear and electron dynamics. We suggest new potential curves for the 32?+ and 42?+ states in HCI+.It is possible to guide slow atoms along magnetic potentials like light is guided in optical fibers. Quantum mechanics dictates that matter can show wave properties. A proposal for a multi mode matter wave interferometer on an atom chip is studied by solving the time-dependent Schrödinger equation in two dimensions. The results verifies a possible route for an experimental realization.An improved representation for wave functions using a discrete set of coherent states is presented. We develop a practical method for computing the expansion coefficients in this non-orthogonal set. It is built on the concept of frames, and introduces an iterative method for computing a representation of the identity operator. The phase-space localization property of the coherent states gives adaptability and better sampling efficiency.