>>12854784You should definitely always think of any Hilbert space in terms of L^2(R^n) with the standard complex-valued inner product, because every other separable Hilbert space is either finite dimensional or L^2(R). In fact, you could just think about l^2(Z) if you want. Or you can think about L^2([0,1]). Pick the comfiest Hilbert space for you, and remember that every other useful Hilbert space is identical to this Hilbert space under a suitable change of basis.
