两体问题 H ++U(5:- 2me 2mN h 2x+U(5。-xDH(x2) 文,XN Er Y(YeIN
两体问题 ( , ) ( )] ( , ) 2 2 [ ( ) 2 2 2 2 2 2 2 2 T e N e N e N x N x e e N N N e e E x x U x x x x m m U x x m p m p H e N = − − + − = + + −
质心坐标与相对坐标 M=mee +Nn M=m十mN Mr+V
质心坐标与相对坐标 X x N x X x e x e N e N e e N N M m M m M m m x x x MX m x m x N e = = = + = + = − = +
V2+U( 2M =m2m(ml2+mN),(x,xN)=Φ(元,X 2Mx2 Vx+UCrDJap(,X E7①(x,X)
( , ) ( )] ( , ) 2 2 [ /( ), ( , ) ( , ) ( ) 2 2 2 2 2 2 2 2 2 2 E x X U x x X M m m m m x x x X U x M H T X x e N e N e N X x = − − + = + = = − − +
分离变量 ①(x,X)=V(x)(X) -V32+(戏)v(x)=Ev(x) Vxo(x)=cEr- E)(X) 2M
分离变量 ( ) ( ) ( ) 2 ( )] ( ) ( ) 2 [ ( , ) ( ) ( ) 2 2 2 2 X E E X M U x x E x x X x X X T x − = − − + = =
相对运动 2Ay+()(x)=Ev(x) y(x)=R(r)Im(0, o)=r(r Ym(e,g) l(l+ x+[+2(E一U()) x=0 x->0,F->0;7->∞
相对运动 1 0, 0; ] 0 ( 1) ( ( )) 2 '' [ ( , ) ( ) ( ) ( ) ( , ) ( )] ( ) ( ) 2 [ 2 0 2 2 2 2 = → → → = + + − − = = − + = dr r r r l l E U r Y r r x R r Y U r x E x l m l m