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Normal order of A + B

  1. Feb 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Hi, guys, I just wondering what's the normal order of A +B

    2. Relevant equations

    if N[A+B]=N[A]+N
    then I have
    [itex]N[aa^{\dagger}]=N[1-a^{\dagger}a]=1-a^{\dagger}a[/itex]
    however we know that
    [itex]N[aa^{\dagger}]=-a^{\dagger}a][/itex]
    what's wrong?

    3. The attempt at a solution

    another example,
    [itex]N[aa^{\dagger}b^{\dagger}b]=N[(1-a^{\dagger}a)b^{\dagger}b]=b^{\dagger}b+a^{\dagger}b^{\dagger}ab[/itex]

    thank you!
     
  2. jcsd
  3. Feb 18, 2013 #2

    George Jones

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    Staff Emeritus
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    Gold Member

    [itex]N \left[ 1 \right] = N \left[ aa^\dagger + a^\dagger a \right][/itex] and linearity gives?
     
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