12. An­gu­lar mo­men­tum

The quan­tum me­chan­ics of an­gu­lar mo­men­tum is fas­ci­nat­ing. It is also very ba­sic to much of quan­tum me­chan­ics. It is a model for deal­ing with other sys­tems of par­ti­cles

In chap­ter 5.4, it was al­ready men­tioned that an­gu­lar mo­men­tum of par­ti­cles comes in two ba­sic kinds. Or­bital an­gu­lar mo­men­tum is a re­sult of the an­gu­lar mo­tion of par­ti­cles, while spin is built-in an­gu­lar mo­men­tum of the par­ti­cles.

Or­bital an­gu­lar mo­men­tum is usu­ally in­di­cated by ${\skew 4\widehat{\vec L}}$ and spin an­gu­lar mo­men­tum by ${\skew 6\widehat{\vec S}}$. A sys­tem of par­ti­cles will nor­mally in­volve both or­bital and spin an­gu­lar mo­men­tum. The com­bined an­gu­lar mo­men­tum is typ­i­cally in­di­cated by

$${\skew 6\widehat{\vec J}}={\skew 4\widehat{\vec L}}+{\skew 6\widehat{\vec S}}$$

How­ever, this chap­ter will use ${\skew 6\widehat{\vec J}}$ as a generic name for any an­gu­lar mo­men­tum. So in this chap­ter ${\skew 6\widehat{\vec J}}$ can in­di­cate or­bital an­gu­lar mo­men­tum, spin an­gu­lar mo­men­tum, or any com­bi­na­tion of the two.