  One of the key features of quantum mechanics is the interference of
probability amplitudes. The reason for the appearance of interference is
mathematically very simple. It is the linear structure of the Hilbert space
which is used for the description of quantum systems. In terms of physics we
usually talk about the superposition principle valid for individual and
composed quantum objects. So, while the source of interference is
understandable it leads in fact to many counter-intuitive physical phenomena
which puzzle physicists for almost hundred years.
  The present thesis studies interference in two seemingly disjoint fields of
physics. However, both have strong links to quantum information processing and
hence are related. In the first part we study the intriguing properties of
quantum walks. In the second part we analyze a sophisticated application of
wave packet dynamics in atoms and molecules for factorization of integers.
  The main body of the thesis is based on the original contributions listed
separately at the end of the thesis. The more technical aspects and brief
summaries of used methods are left for appendices.

Quantum Physics