Quantum-mechanical two-center problem for the Dirac equation

The Dirac equation for the potential of two Coulomb centers is considered. The region of distances fairly far from the centers is investigated. A method is proposed for constructing and investigating numerically the solutions of the Dirac equation with this potential. With a view to finding solutions in the region near the charges, the Dirichlet problem is formulated for a system of partial differential equations. The results are given of the numerical calculation of the lower electron level for some values of the charges and the distances between them.