where μ μ 0 is the vacuum permeability, μ μ B is the Bohr magneton, g is the g-factor, e is the elementary charge, m e is the electron mass, L is the orbital angular momentum operator, S the spin and r ⊥ ⊥ is the component of the position operator orthogonal to the magnetic field. The Hamiltonian has three terms, the first one H 0 is the unperturbed Hamiltonian without the magnetic field, the second one is proportional to H , and the third one is proportional to H 2 . In order to obtain the ground state of the system, one can treat H 0 exactly, and treat the magnetic field dependent terms using perturbation theory. Note that for strong magnetic fields, Paschen-Back effect dominates.