Question

Consider an electron in the hydrogen atom. The electron is initially in the ground state.

If spin-orbit coupling is considered, the state of the electron can be written as | j, m_j〉. Give the values of the quantum numbers j and m_j and determine the term symbol of the ground state of the system.

Answer 1

The calculations are given below. One important thing is that I have used the letters l,s and j to represent orbital,spin and total angular momentum respectively which is the correct convention for one electron. For multi-electronic system the letters L,S and J have to be used instead of l,s and j respectively.