# Expected value in quantum

xdeimos

xdeimos
quantum expected value

1. why <x> is squeez between ψ* and ψ what we doing this?
2. for <p> [h/i d/dx ] is sqeeze between ψ* and ψ why is that?
3. if you put latter operator between ψ* and ψ what is going to happen?

thank you

Mentor
Its easier to see in the Dirac notation - E(A) = <u|A|u>

But that is only a special case valid for so called pure states - the full rule is E(A) = Trace(PA) where P is a positive operator of unit trace which is the correct definition of a quantum state - pure states |u><u| are a special case. For pure states Trace(|u><u| A) = <u|A|u>

As to why that formula check out Gleason's Theorem:
http://kof.physto.se/theses/helena-master.pdf [Broken]

Thanks
Bill

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