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10: Addition of Angular Momentum

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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 Section [s10.4].) To these we must now add the two quantum numbers \(s\) and \(m_s\) that 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?