# Parity operators and anti commutators

1. Feb 2, 2012

### qtm912

I am trying to understand the following which is proving difficult:

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.

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