The quadratic Zeeman effect for highly excited hydrogen atoms in weak magnetic fields

The hydrogen Rydberg states in the presence of weak magnetic fields are analytically investigated by using quantum mechanical first-order perturbation theory. The unperturbed hydrogenic wavefunctions, which diagonalise the quadratic Zeeman interaction within the subspace of states with fixed principal quantum number n, are obtained by separation of variables on the Fock hypersphere in momentum space. By considering n as a large parameter, the comparison equation method is employed to find the uniform asymptotics of eigenfunctions and asymptotic expansions of quadratic Zeeman energies corresponding to the outermost components of the Zeeman n manifold. The results obtained are compared with other theoretical predictions.