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Bogoliubov superfluidity Hamiltonian

  1. Oct 9, 2009 #1
    [tex]\hat{H}=\sum_{\vec{p}}\frac{p^2}{2m}\hat{b}^+_{\vec{p}}\hat{b}_{\vec{p}}+\frac{1}{2V}\sum_{\vec{p}_1,\vec{p}_2,\vec{p}_3}W(\vec{p}_1-\vec{p}_3)\hat{b}^+_{\vec{p}_1}\hat{b}^+_{\vec{p}_2}\hat{b}_{\vec{p}_3}\hat{b}_{\vec{p}_1+\vec{p}_2-\vec{p}_3}[/tex]

    Is this correct form or maybe?

    [tex]\hat{H}=\sum_{\vec{p}}\frac{p^2}{2m}\hat{b}^+_{\vec{p}}\hat{b}_{\vec{p}}+\frac{1}{2N}\sum_{\vec{p}_1,\vec{p}_2,\vec{p}_3}W(\vec{p}_1-\vec{p}_3)\hat{b}^+_{\vec{p}_1}\hat{b}^+_{\vec{p}_2}\hat{b}_{\vec{p}_3}\hat{b}_{\vec{p}_1+\vec{p}_2-\vec{p}_3}[/tex]

    One form is in book and one in scripts! This is first relation so I'm not quite sure! Thanks for you're answer!
     
  2. jcsd
  3. Oct 9, 2009 #2
    Actually both forms are correct. In the second, the author assumes the unit cell volumn is one, so N indicates the total volumn V.
     
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