Basic question

can anyone tell me what one means by these bracket

Code:

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[tex]
      \langle\psi(r)\psi^*(r) \rangle
      [/tex]

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, is it integral or what?????and is there any idea how to calculate this integral

Code:

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[tex]
      \int\int{\mid\langle\psi(r)\psi^*(s)\rangle\mid}^  2 dr ds
      [/tex]

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I suppose this is quantum mechanics?

The angled brackets used in the combination you wrote usually indicate an average value, and in QM they denote the expectation value of an operator.

You can also use them for things like writing the state of a particle, for example |a> means a particle in state a.
Or you can use them for an inner product:
< f | g > means the inner product of functions f and g, often defined by the integral over f*(x) g(x) dx, (sometimes including a positive weight function)

That being said, I have no clue what the operator (psi psi*) would be... Never seen it before (although I'm not too advanced at QM to be honest).
The integral looks a bit like the calculated of an expectation value, except that you also use the brackets inside the integral, which makes zero sense to me. I also don't understand the double integral.

Where did you get these from? In what context are you using them? What are psi(r) and psi(s), what are r and s, etc..? You will need to specify alot more information.

Quote:

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Originally Posted by NickThissen

I suppose this is quantum mechanics?

The angled brackets used in the combination you wrote usually indicate an average value, and in QM they denote the expectation value of an operator.

You can also use them for things like writing the state of a particle, for example |a> means a particle in state a.
Or you can use them for an inner product:
< f | g > means the inner product of functions f and g, often defined by the integral over f*(x) g(x) dx, (sometimes including a positive weight function)

That being said, I have no clue what the operator (psi psi*) would be... Never seen it before (although I'm not too advanced at QM to be honest).
The integral looks a bit like the calculated of an expectation value, except that you also use the brackets inside the integral, which makes zero sense to me. I also don't understand the double integral.

Where did you get these from? In what context are you using them? What are psi(r) and psi(s), what are r and s, etc..? You will need to specify alot more information.

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yes it is QM context and I am new to this area, so <psi(r)> is the expectation value of what?............here I am trying to understand how they calculate the ensemble variance.....<\psi \psi*> there is no comma in between..... .I add the equation as in LaTex.......
\eta[\psi]=\int\{\mid\psi(r)\mid\}^2 dr
Var(\eta)=2\iint\{\langle\mid\langle\psi(r_1)\psi^*(r_2)\rangle\rangle\mid}^2 dr_1 dr_2
then it is easy to obtain the following composition rule
\int\langle\psi(r_1)\psi^*(r)\rangle\langle\psi(r)\psi^*(r_2)\rangle dr=1\N\langle\psi(r_1)\psi^*(r_2)\rangle

I'm sorry, I have no clue what you are after... If you are really new to QM then you should probably start way more at the basics! I have succesfully followed a 'basic QM' course at my university and am at the moment following the second course, but I still have never seen what you are asking.
(Yes, I do know what LaTeX is so it's not the latex text that is putting me off :p)

Maybe you can try asking it on this physics forum (in the appropriate QM thread or homework help threads):
http://www.physicsforums.com/
(I don't know if this is considered advertisement..? I hope not, it's not my forum or anything, I'm just pointing him to a place where he has more chance of finding someone who can help him)

That LaTeX code doesn't parse terribly well (after fixing a few errors there were still <'s and |'s misplaced several times), but even if it did to echo Nick I think you'd have much better luck on a Physics board.

The expectation value and bra-ket notation are what Nick referred you to.

I'd be very surprised if your professor (I'm assuming you're taking a QM course) didn't go over this....

appreciate your time.:), actually I came across these material when I try to do peace of writing about the Normalization and how is related to the variance of Gaussian ensembles.....it seems to be statistical mechanics......unfortunately I tried in Physics forum but I have not get any reply...