# What do you need to establish that spin is conserved?

• I
• Old Person
In summary, there is no classical interpretation of spin, but it is often considered a conserved quantity and a form of angular momentum. However, this is only true in certain situations, as total angular momentum is the true conserved quantity. References, such as Ballentine's "Quantum Mechanics: A Modern Development," provide further explanation and proof of this concept.
Old Person
TL;DR Summary
What do you need to establish that spin is a conserved quantity?
Hi.

Question as in the summary.
Spin has no obvious classical interpretation but it is often a conserved quantity and considered as some sort of angular momentum. What do you need to establish that spin is a conserved quantity? I'm finding references to situations where spin is not a conserved quantity in general but only in some processes. Hence, what is needed to assert conservation?

Any replies or references to existing discussions or proofs would save me time and be appreciated. Thank you for your time.

Old Person said:
Spin has no obvious classical interpretation but it is often a conserved quantity and considered as some sort of angular momentum.
No, spin by itself is not "often" a conserved quantity. Total angular momentum is the conserved quantity. Only in situations where orbital angular momentum is either identically zero or is conserved on its own can spin be considered a conserved quantity by itself.

As for spin being "some sort of" angular momentum, that's much too vague. Spin is whatever part of total angular momentum is not orbital angular momentum. See, for example, Ballentine, Chapter 7.

topsquark, hutchphd, vanhees71 and 1 other person
Thank you. I'll look for that when I get to a library.
Found: "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine.
No great need to reply - I'll assume it's that book unless you say otherwise.

vanhees71
Old Person said:
Found: "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine.
Yes, that's it.

vanhees71

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