Here ω ω 0 := γ γ B 0 is the Larmor precession frequency of the dipole for B 0 magnetic field and σ σ z is z Pauli matrix. So the eigenvalues of H ^ ^ are − − ℏ ℏ 2 ω ω 0 and ℏ ℏ 2 ω ω 0 . If the system is perturbed by a weak magnetic field B 1 , rotating counterclockwise in x-y plane (normal to B 0 ) with angular frequency ω ω , so that B 1 = i ^ ^ B 1 cos ⁡ ⁡ ω ω t − − j ^ ^ B 1 sin ⁡ ⁡ ω ω t , then [ 1 0 ] and [ 0 1 ] are not eigenstates of the Hamiltonian, which is modified into