Schrodinger wave equation/Talk

I'm a bit concerned that the second paragraph does not make sufficiently clear what role the Hilbert space plays: the elements of the Hilbert space describe instantaneous states of the system. The time-dependent wave function Ψ is therefore not an element of the Hilbert space; it is a function with values in the Hilbert space (and domain time)

Ψ : R -> Hilbert space.

It took me a while to figure this out, and I'm not sure that all physists are aware of it; maybe we should explain it in that paragraph?

Also, the notation Ψ = Ψ(r,t) seems to imply that the Hilbert space is the space of square integrable functions, but that is only true in some special one-particle examples. Often, the Hilbert space is a tensor product of several finite- and infinite-dimensional ones, and the elements of it cannot really be thought of as "wave functions" (which is why I quoted that term in the original article). --AxelBoldt