Angular Momentum Operators

Here, the differential operator is given by

(1435) |

where

is times the orbital angular momentum operator of wave mechanics.

The components of are conveniently written in the combinations

Note that only operates on angular variables, and is independent of . It is evident from the definition (1438) that

It is easily demonstrated from Equations (1439)-(1441) that

(1441) |

The following results are well known in quantum mechanics:

In addition,

(1445) | ||

(1446) | ||

(1447) |

where

(1448) |