I'm continuing through Dirac's book, The Principles of Quantum Mechanics. You can view this as a google book in the link below.(adsbygoogle = window.adsbygoogle || []).push({});

http://books.google.com.au/books?id=...page&q&f=false [Broken]

On page 28-29 he proves this Theorem:

If ξ is a real linear operator and

ξ^{m}|P> = 0 (1)

for a particular ket|P>,m being a positive integer, then

ξ|P> = 0

...

And the proof is fine by me except for the first part where he says:

put m = 2 then (1) gives

<P|ξ^{2}|P> = 0 (2)

and goes on to prove it by induction. But I don't see how (2) is 'given' from (1).

Can anyone explain?

If he is relying on assuming (1) is true for some ket |P> and positive integer m, then I just pick m = 1 and it's not a theorem. And besides, in this case he never demonstrates a definite example of the statement being true, which you need to do in induction.

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# A little Bra-Ket notation theorem that I don't get

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