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- Thread starter xdeimos
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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

- #3

bhobba

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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

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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- #4

Khashishi

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The sign of the complex part of the wavefunction also has no real significance. Multiplying a number by its complex conjugate gives the absolute value squared. This is a handy mathematical trick, but there's no reason other than convention to put the conjugate on the left factor or the right factor.

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