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Consider an electron in a hydrogen atom. As we have already seen, the electron's motion through space is parameterized by the three quantum numbers $n$, $l$, and $m$ (see Sect. 9.4). To these we must now add the two quantum numbers $s$ and $m_s$ which parameterize the electron's internal motion (see the previous chapter). Now, the quantum numbers $l$ and $m$ specify the electron's orbital angular momentum vector, ${\bf L}$, (as much as it can be specified) whereas the quantum numbers $s$ and $m_s$ specify its spin angular momentum vector, ${\bf S}$. But, if the electron possesses both orbital and spin angular momentum then what is its total angular momentum?

Richard Fitzpatrick 2010-07-20