dr inż. Michał Piłat | Gdańsk University of Technology

A class of quantum probabilities is reformulated in terms of non-Newtonian calculus and projective arithmetic. The model generalizes spin-1/2 singlet state probabilities discussed in Czachor (Acta Physica Polonica:139 70–83, 2021) to arbitrary spins s. For s → ∞ the formalism reduces to ordinary arithmetic and calculus. Accordingly, the limit “non-Newtonian to Newtonian” becomes analogous to the classical limit of a quantum theory

Focusing on the noble gases, we calculate the scattering potential using the Dirac-Coulomb Hamiltonian supplemented with a model polarization potential. We determine the scattering lengths using two methods, namely phase shifts for very small scattering energies and the shape of the wave function for zero scattering energy. We compare our theoretical electron scattering length results on Ar, Kr and Xe atoms with existing experimental...

The aim of this dissertation is to present the theory of relativistic electron-atom scattering at low energies. This work focuses on the theory of calculation of scattering length and how it can be formulated in the relativistic quantum theory. An approximate solution to the Dirac equation with polarization potential behaving as r-4 is presented as well as the formulation of the effective range theory for Dirac’s equation. Those...