An approximate relation between the energy levels of a particle in a field of given potential energy, calculated on the relativistic and non-relativistic theories

The relativistic Hamiltonian H for a particle in a field of potential energy V is given, in atomic units, by the formula where any ρ commutes with any σ, any σ anticommutes with any other σ, ρ 1 anticommutes with ρ 3 and