My textbook "The physics of quantum mechanics" by James Binney and David Skinner, describes the pseudo-vector operators [itex]\vec{J}[/itex], [itex]\vec{L}[/itex] & [itex]\vec{S}[/itex] as generators of various transformations of the system. [itex]\vec{J}[/itex] is the generator of rotations of the system as a whole, [itex]\vec{L}[/itex] is the generator of displacement of the system around circles without rotations, and [itex]\vec{S}[/itex] is the generator for changes of orientation that are not accompanied by any motion of the system as a whole.(adsbygoogle = window.adsbygoogle || []).push({});

In the book, [itex]\vec{J}[/itex] is defined as the generator of rotations, while [itex]\vec{L}[/itex] is defined by [itex]\vec{L} = \vec{x} \times \vec{p}[/itex], and then [itex]\vec{S}[/itex] is defined by [itex]\vec{S} = \vec{J} - \vec{L}[/itex]. My issue with this is that [itex]\vec{L}[/itex] seems to have been defined by classical analogy, which leads me to question how fundamental the division of angular momentum into orbital and spin is. The book later describes spin as intrinsic to the particle, which implies that it is, in fact, a fundamental division. Assuming it is fundamental, can you predict that mathematically, or is it an observational fact?

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# I Is J=L+S fundamental?

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