On the quadratic Zeeman effect in highly excited states of hydrogen and alkali-metal atoms

Diamagnetic splitting of Rydberg atomic states in weak magnetic fields is studied. The zero-order perturbation equation is solved by the discrete WKB method, the quantum defect is taken into account through the boundary condition. Effects of tunnelling are considered. A semiclassical quantisation condition is obtained determining eigenvalues as functions of quantum numbers, field and quantum defects of the atom in question.