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[Q]Momentum eigenstate normailization

  1. Oct 12, 2008 #1
    Hi

    I use liboff quantum mechanics text book fourth edition.

    5.25 fomula of 122 page is [itex] \frac{1}{\sqrt{2\pi}}e^{ikx} [/itex]

    I thought it is nomalized, but i don't know exactly why [itex] \sqrt{2\pi} [/itex] is denominator.

    I think it seemed to be linked Dirac-delta function [itex] \int_{\infty}^{\infty}\frac{1}{2\pi}e^{i(k-k^{'})x} = \delta(k-k^')[/atex] but i have no idea what is going on exactly.

    Please Help me

    Thank for reading this question.
     
  2. jcsd
  3. Oct 12, 2008 #2

    CompuChip

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    I think it is because of his definition of Fourier transform. Different people use different conventions. In the end, they are all equivalent of course and should give the same results.

    See, for example this link ("Other conventions" section).
     
  4. Oct 12, 2008 #3
    Thank you so much that i found Fourier transform is included general innerproduct

    in some mathematical space as l Fourier transform is just analogous to vector

    innerproduct between momentum eigenfunction and statefunction. thank you.

    but i have one questiong. what is hilbert space in which general vectorproduct is

    defined?
     
  5. Oct 13, 2008 #4

    George Jones

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    What do you mean by general vector product?
     
  6. Oct 13, 2008 #5
    It means innerproduct such as [tex]<\varphi_{k}|\varphi{_{k^'}}> [/tex] i described

    product of this form as more general form of 'vector innerproduct in normal vector space'
     
    Last edited: Oct 13, 2008
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