The perturbation of boundary conditions for differential equations of atomic theory

A perturbation of boundary conditions for single-electron radial orbitals in the Schroedinger, Klein-Gordon, Dirac and Hartree-Fock equations is considered. The perturbation is also discussed of boundary conditions at the origin of coordinate system for the isotopic shift of energy levels because of the finite dimensions of a nucleus. The coordinate transformation is applied which allows to reduce a small variation of the boundary condition to a perturbation of potential which makes it possible to apply later the conventional perturbation theory. The effect of the nuclear volume is considered by means of combining the relativistic electron radial orbitals near and inside a nucleus, and then a small variation of the nuclear radius can be reduced to a potential perturbation. The results represent the analytical expressions for corrections for energy and other quantities in the first order of the perturbation theory