It is very difficult to solve the Schrodinger equation. However, it is even harder to solve its relativistic version: the Dirac equation! Using the two-electrons-on-a-sphere model, which is exactly solvable in the Schrodinger framework, I will investigate the possibility of exact analytical results within the Dirac treatment. I am particularly interested in the behaviour of the wave function when two electrons "touch" each other. This will lead to a deeper understanding of relativistic effects in many-electron systems.