The universal way to probe a physical system is to scatter a particle or radiation off the system.The results of the scattering are governed by theinteraction Hamiltonian of the physical system and scattered probe. An object of the investigation can be a hydrogen atom immersed ina laser field, heavy nucleus exposed to a flux of neutrons, or space-time metricperturbed by the stress-energy tensor of neutrino flux in the early Universe. This universality of scattering process designates the {\it Scattering Matrix}, defined as the unitary matrix of the overlapping {\it in} and {\it out} collision states, as the central tool in theoretical physics.In this Thesis we present our results in atomic physics, nuclear physics, and cosmology. In these branches of theoretical physics the key element that unifies all of them is the scattering matrix.Additionally, within the scope of Thesis we present underlying ideas responsible for the unification of various physical systems.Within atomic physics problems, namely the axial anomaly contribution to parity nonconservation in atoms, and two-photon resonant transition in a hydrogen atom, it was the scattering matrix which led to the Landau-Yang theorem, playing the central role in these problems. In scattering problems of cosmology and quantum optics we developed and implementedmathematical tools that allowed us to get a new point of view on the subject.Finally, in nuclear physics we were able to take advantage of the target complexity in the process of neutron scattering which led to the formulation of a new resonance width distribution for an open quantum system.
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