Recent content by einheit

Thanks, again, that makes the problem even clearer.

Thanks, PeroK, I guess that's my problem.

Yeah, exactly. Please see reply to vanhees71, where I elaborated all that, partly in reply to your post. But I meant that I'm "combining" all the system's observables to construct the Hilbert space representing its space of physical states. And then, presumably, any pure state...

That alone would answer my question. But excuse me for disagreeing. For example, an electron is spin-1/2 but also has energy. Indeed, just about all systems have Hamiltonians, whereby there's pretty much always "something else." Usually lots of other things, i.e., other observables. And it's...

To elaborate that summary a bit, suppose ##\mathcal H## is the Hilbert space of the particle, with ##\mathcal{H}_2\subseteq\mathcal{H}## its two-dimensional spin subspace. Now consider any ##|x\rangle\in\mathcal{H}## such that ##|x\rangle\perp\mathcal{H}_2##, i.e., ##\forall ~...