Question

In strong Zeeman effect why the total angular momentum is not conserved , but Lz and Sz are conserved ?

Answer 1

Since we know that for a rotationally invariant hamiltonian, we can say that the total angular momentum is conserved for an isolated atom. This is the necessary condition.

Now, In Zeemen's effect, When the atom is immersed in an external magnetic field, The Hamiltonian contains Bz component due to which it expiriences a torque making the system still cylindrically symmetric about z-axis due to which total energy of the system does not change & hence making Lz & Sz conserved.