In the proposed talk, a new methods of quantum mechanics for nuclear scattering and decays (called as method of Multiple Internal Reflections or method MIR) will be presented. In problems of alpha-decay, decay of nuclei with emission of protons, capture of alpha-particles by nuclei it allows to study strong quantum phenomena with high precision and tests, to investigate realistic potentials [1, 2].
That method is further applied for quantum cosmology, where idea of tunneling is investigated in description of evolution of Universe in the first stage. Appling for the Friedmann - Robertson - Walker model with quantization in the presence of positive cosmological constant, radiation and the generalized Chaplygin gas [3], the method allows to study some quantum phenomena of Big Bang.
Last part of talk is devoted to question of relativization in quantum mechanics, i.e. question on how to connect quantum mechanics and special relativity. Starting from Dirac equation for one fermion with addition of potential, new Hamiltonian is formulated with orientation of relativistic collisions of nuclei, where formalism allows to study quantum phenomena with high precision and tests (like method MIR above).