Momentum eigenstate

  • Thread starter imagemania
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  • #1
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Homework Statement


I am trying to translate what is meant by:
<psi | p | psi>
<psi|p^2|psi>
<psi | x | psi>
In a mathematicaly context as shown by this link:

http://answers.yahoo.com/question/index?qid=20110521103632AASz9Hm [Broken]


Can anyone specify what these mean?

Thanks!
 
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Answers and Replies

  • #2
tiny-tim
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hi imagemania! :smile:

<| denotes a row vector

|| denotes a matrix

|> denotes a column vector :wink:
 
  • #3
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Ok, but im still not following how he got one for the first question:
<psi | p | psi> = 0

for the integral:
[tex]\psi = \int_{-\infty}^{\infty} {e}^{-\alpha {(k-{k}_{0})}^{2}}{e}^{ikx} dk[/tex]

Thanks
 
  • #4
tiny-tim
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not following you …

ψ is as given, and p is the momentum operator :confused:
 
  • #5
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Perhaps i'll ignore that post and go back to the fundamental question. From my understanding,
[tex]\bar{p}=\frac{hk}{2 \pi}[/tex]. Knowing [tex]\psi[/tex] is there a way to deduce a better answer to [tex]\bar{p}[/tex] or is it just as I said here?

I am also unsure about the equation for mean value of x.

Thanks :)
 
  • #6
vela
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It's Dirac notation. For an operator A, you can write
[tex]\langle \psi | \hat{A} | \psi \rangle = \int \psi^*(x)\hat{A}\psi(x)\,dx[/tex]
You've been given the wave function. What you need to do next is look up how to express the operators x, p, and p2 appropriately.
 

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