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Nov 30, 2013 at 5:53 comment added ChickenGod Right. I actually wanted to add the extra constraint that $c_\alpha$ acting on an $n_\alpha = 0$ state gives $0$, but I forgot to type that in. Thanks though!
Nov 30, 2013 at 1:03 comment added Selene Routley +1 Most excellent point. I was actually "adding the constraints in by hand" in my own answer without even realizing I was doing it. Indeed I've just realised that I've always subconsciously been doing it with problems of this kind: I'm ashamed to say that I'd never even really noticed what you say before: the $\sqrt{n}$ shuts the "downstepping" of the annihilation operator down automatically at $n=0$.
Nov 29, 2013 at 12:03 history answered Trimok CC BY-SA 3.0