Theoretical Description of Relativistic Terms of a Hydrogen Atom in a Magnetic Field: A Variational Approach in the Basis of Hydrogen-Like Spinors

Abstract

The incomplete diagonalization of a Dirac Hamiltonian in the basis of the states of an unperturbed atom is used to obtain solutions to the Dirac equation for a hydrogen atom in a constant uniform magnetic field and a wide range of changes in strength. The resulting finite expressions for the matrix elements of the perturbation operator of an arbitrary hydrogen-like atom are used to estimate the action of operators in minimizing the energy dispersion functional. The approach allows precise estimates of the energy of the ground state and values of the energies of transition that are in good agreement with results from earlier studies. It is shown that the proposed technique for minimizing the energy dispersion functional allows the incomplete diagonalization of operators for an arbitrarily chosen block of target states, provided that the initial approximation is correct.