Hartree-Fock approximation Energy density(without retardation n effect) E=<|H>=<T>+<V Perform operator computatio ns in potential energy <O>=<d 6, b-aa b, ba d> <1b 6. 6 P2-q, 42 P2, P1+q a1 2 P2, a2 P1+g aj/P1 P lbp, as n切l.>+<身b=bbn1 Using the projection operator 2I><d1=l, it becomes <O>=62Q2Onx+∑<|bt=a2b2a21>中 P1+q, ai Pi,a Hartree Fock approximat ion: taking i=0& omitting all intermedia te states Pb P><pIb. b P1+q, a, lo =asO aSn,nO+ Fock term hartree term May 9, 2013@ USTCMay 9, 2013 @ USTC Hartree-Fock approximation Fock term Hartree term | | | | ˆ Hartree Fock approximat ion : taking i 0 & omitting all intermedia te states | | | | ˆ Using the projection operator | | 1, it becomes | | | | | ( ) | | | ˆ Perform operator commutatio ns in potential energy : 2 1 | | Energy density (without retardatio n effect) : 2 1 1 2 2 1 2 2 1 1 2 1 1 2 2 1 2 2 2 2 1 , 1 1 2 1 1 2 2 1 2 2 2 2 1 , 1 1 1 1 , 1 1 2 1 1 2 2 1 2 2 2 2 1 1 , 1 2 2 2 1 1 2 2 2 1 , 1 2 2 2 2 1 , , , ,0 0 1 , , , 0 , , 0 0 , 0 1 , , , 0 , , , i 0 1 , , 0 0 , , , 1 0 , , 0 1 0 , , , , , 0 1 0 , , , 0 0 = + = +   = +     =   = +       = = −   +   = −  −   =  =  =  +     +   + +   + −  + +   + −  + +  + −  +  + +  + −  + −  + +  +  +  +  +    a a a a p p q a a a a a a a a p p q p q a p a p a i a a a a p p q p q a p a i i p a i i p a p a a a p p q p q a p a p a p q a p p q a a p a p a p q a p a p a O b b b b O b b b b b b b b b b b b b b O b b b b H T V p q a p q a p q a p q a p q a                                      q