Because of the definition of k, this result holds for both signs of k, and (c) is proved.

Finally, to prove (b), we will first show that a ■ has angular mo mentum quantum numbers j and m and opposite parity from y^if)- This will establish that

where Nj is a constant of proportionality. Then we will show that Nj = —1.

To prove (6.23), it is sufficient to show that J1 commutes with cr • r and that the spatial parity operator anticommutes with cr ■ r:

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