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## Main Question or Discussion Point

[tex]\hat{H}_{BCS}=\sum_{\vec{p},\sigma}\epsilon(\vec{p})\hat{a}^+_{\vec{p},\sigma}\hat{a}_{\vec{p},\sigma}+\sum_{\vec{p},\vec{p}'}V(\vec{p},\vec{p}')\hat{a}^+_{\vec{p}\uparrow}\hat{a}^+_{-\vec{p}\downarrow}\hat{a}_{-\vec{p}'\downarrow}\hat{a}_{\vec{p}'\uparrow}[/tex]

What is the meaning of the terms [tex]\hat{a}^+_{\vec{p}\uparrow},\hat{a}^+_{-\vec{p}\downarrow}[/tex]... ?

If I work mean- field approximation

[tex]\hat{H}_{BCS}=\hat{H}_0+\hat{H}_2+\delta\hat{H}[/tex]

What is the procedure to find terms [tex]\hat{H}_0[/tex], [tex]\hat{H}_2[/tex], [tex]\delta\hat{H}[/tex]?

What is the meaning of the terms [tex]\hat{a}^+_{\vec{p}\uparrow},\hat{a}^+_{-\vec{p}\downarrow}[/tex]... ?

If I work mean- field approximation

[tex]\hat{H}_{BCS}=\hat{H}_0+\hat{H}_2+\delta\hat{H}[/tex]

What is the procedure to find terms [tex]\hat{H}_0[/tex], [tex]\hat{H}_2[/tex], [tex]\delta\hat{H}[/tex]?