变分原理 薛氏方程的变分表达 H=(,HP) SF-is(p, p)=O (H2)=1
变分原理 ◼ 薛氏方程的变分表达 ( , ) 1 ( , ) 0 ) ˆ ( , = = − = = H E H H H
选择定理 HUi =Eyi E≤E1≤E,≤E2≤ (v,)=o∑|v,v|=1 The min imum of(u, Hu/y, u)is (Eo, ify can be any state (El, ify can be any state that satisfies condition (V,yo=0 (3)
选择定理 (3).... ( , ) 0; (2) , (1) , ; )/( , ) ˆ min ( , ( , ) 1 .... 0 1 0 0 1 2 3 = = = = condition E if can be any state that satisfies E if can be any state The imum of H is E E E E H E i j i j i i i i i
里兹变分 ■选择含参数的试探函数 d=Φ(C1,C2…) ■计算期望 H=(d,)(d2) =H(C1,C22…… 变分求极值
里兹变分 ◼ 选择含参数的试探函数 ◼ 计算期望 ◼ 变分求极值 ( , ,...) = C1 C2 ( , ,...) )/( , ) ˆ ( , H C1 C2 H H = =
OHr/C;=0,i=1,2,3, 解出参数C; 代回得近似值 E=H(C1,C"2)
◼ 解出参数Ci ’ ◼ 代回得近似值 H / C = 0,i = 1,2,3,.... i ( ' , ' ,..) E = H C 1 C 2
氦原子基态能量 (V1+V2)-2e(-+-) xz2=2,2=|元1-x2
氦原子基态能量 1 2 2 1 2 1 2 1 2 2 0 1 2 2 1 2 2 2 2 2 1 2 , , ˆ ) 1 1 ( ) 2 ( 2 r x r x r x x r e H r e r r H e = = = − = + + = − + − +
不计排斥项时 平(x1,x2)=v10(1y10(2) 3 1+n 2
不计排斥项时 , 2 ( , ) ( ) ( ) ( ) 3 0 3 1 2 100 1 100 2 1 2 0 = = = − + e z a z x x x x r r a z