Changes

The eigenstates of the reflectivity operator are formed out of states of good ''J,m'' as follows.

The eigenstates of the reflectivity operator are formed out of states of good ''J,m'' as follows.

:<math>| J m \epsilon \rangle = | J m \rangle + \epsilon P (-1)^{J-m} | J \; -m \rangle    </math>

:<math>| J m \epsilon \rangle = | J m \rangle + \epsilon P (-1)^{J-m} | J \; -m \rangle    </math>

where &epsilon;=&plusmn;1, such that

where &epsilon;=&plusmn;1 for a bosonic system and &epsilon;=&plusmn;i for a fermionic system.  It follows that

:<math>\mathbb{R}| J m \epsilon \rangle =  \epsilon (-1)^{2J} | J m \epsilon \rangle </math>

:<math>\mathbb{R}| J m \epsilon \rangle =  \epsilon (-1)^{2J} | J m \epsilon \rangle </math>