- #1

JDoolin

Gold Member

- 720

- 9

What does a "state vector" look like?

It looks like |α> or |β> But more than that... It is a complex vector in Hilbert space?

Now, you get "observables" from state-vectors by performing operators on them. So the state-vector contains all the information, but if you want to know the momentum, you do the momentum operator, if you want to know the spin, you do the spin operator, if you want to know the (mass?) you do the mass operator?

And then there are three spin operators, right? S

_{z}, S

_{x}, S

_{y}, and these are called "incompatible observables" because they do not commute. That is S

_{z}S

_{y}≠S

_{y}S

_{z}

I'll stop there for now, in case I'm completely on the wrong track...

But what does this symbol, an equals-sign with a dot over it, mean?

[tex]\doteq[/tex]