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Local density of number of photons

  1. Feb 27, 2010 #1
    Number of photons operator can be define as follows: [tex]\sum a_k^\dagger a_k [/tex].
    Is it possible to define this operator locally and obtain operator [tex] \hat{n}(x,y,z)[/tex]of local density of number of photons so that [tex] \langle \psi |\hat{n}(x,y,z)|\psi\rangle = \rho(x,y,z)[/tex]. Thanks for reply.
  2. jcsd
  3. Feb 27, 2010 #2


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    Science Advisor

    It can be done. It is [tex] \psi^{\dagger}(x,y,z)\psi(x,y,z)[/tex], where [tex]\psi(x,y,z)[/tex] is essentially the Fourier transform of [tex] a_k [/tex].
    For details, see
    http://xxx.lanl.gov/abs/0904.2287 [to appear in Int. J. Mod. Phys. A]
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