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Homework Help: Two slit experiment - quantum theory - problem

  1. May 15, 2007 #1
    Hi, I'm new and I'm from Poland.
    I have problem with equation(average number of photons registered behind pinhole 1 in two slit experiment):
    [tex]\bar{n}_1=\langle n|a_{1}^{+}a_{1}|n\rangle=\frac{\langle 0|(a^{+})^{n}a_{1}^{+}a_{1}(a^{+})^{n}|0\rangle}{n!}[/tex]
    using:
    [tex]a^{+}=\frac{(a_{1}^{+}+a_{2}^{+})}{ \sqrt{2}}[/tex]
    and
    [tex]a=\frac{(a_{1}+a_{2})}{\sqrt{2}}[/tex]
    and
    [tex]|n\rangle=\frac{1}{\sqrt{n!}}(a^{+})^{n}|0\rangle[/tex]
    and using usual creation and destruction oprator properties, to give finally :
    [tex]\bar{n}_1=\frac{1}{2}[/tex]

    I have no idea how to do it...
    Big thnx
     
  2. jcsd
  3. May 16, 2007 #2
    Welcome
    Hi i think that you must specify that whether there is a detector or not at any of the slits and whether the other slit is open or not.Other wise refer volume three of feynman lectures
     
  4. May 19, 2007 #3
    We have a stream of photons incident on a pair of identical pinholes. We assume that only a single mode of the cavity (cavity formed by the lens and the first screen) is excited, with photon creation and destruction operators

    [tex]a^{+}[/tex]

    and

    [tex]a[/tex]

    We suppose that the two piholes provide the only means for photons in the cavity.For pinholes of equal size, the incident photons are equally likely to be registered in mode 1 or 2.

    Still I don't know how to prove it.
    I will be grateful for help.
     
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