Abstract

In this dissertation I present a high-precision (15, 18 or 33 decimal places) C++ implementation of quantum dynamics time propagation algorithms for both time-independent and time-dependent Hamiltonian with an inhomogeneous source term. Moreover I present an extension of both algorithms for time propagation to handle arbitrary number of coupled electronic levels. I have performed a careful validation of these implementations comparing my results with numerous reference results such as: a forced harmonic oscillator with an inhomogeneous source term or an atom in an intense laser field. Next, I apply these new algorithms to calculate the rovibrational predissociation in the KLi molecule and compare it with experiment. In doing so I have shown that the KLi quasi-bound state decays exponentially in time and I have described a robust method to calculating the widths of quasi-bound vibrational levels. Also I have calculated the decay in the NaRb dimer using three coupled electronic states. I have performed a fit of this decay to a modified power-law and I have shown that this fit is better than a fit to the exponential decay. I hope that those results are of considerable relevance to the design of experiments.

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