I am trying to understand the following which is proving difficult:(adsbygoogle = window.adsbygoogle || []).push({});

It is found that (and the proof here is clear)

[P, Jj] anticommutes with Vi

Where P = parity operator

Jj and Vi are the j th and i th components of the angular momentum vector and an arbitrary vector respectively.

It is then stated that because P has the same anticommuting property, that [P,Jj] must be proportional to P ,ie that

[P,Jj] = λP

Where λ is a scalar and the same for all j

I am unclear how this is imputed. Why should they be proportional.

Thanks in advance

(ref is Binney and Skinner QM book Chapter 4 page 66

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# Parity operators and anti commutators

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