Zaph

I think I do agree with J. Delaney here. When talking about physical states we usually assume they have norm 1, or at least can be normalized by multiplication with some scalar. When an annihilation operator acting on such a state gives zero for all orbitals, that state must be empty, which is a contradiction to being an N-particle state. I think it would be very beneficial to change the formulation into “Vector in an N-particle-Hilbert space”, so people don’t assume it should lie on the sphere-surface.

@tparker the "$N>0$" was edited in after the comment of TobiasFünke. Calling the zero element of the Hilbert-space a state or not seems like a rather linguistic discussion, how would you refer to it?

@Rasmus that seems like producing a contradiction, if you did that.