两体问题 e H +U/ 2me 2mN h"xe 2y 2 V +U N e
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=meXe + IN N M=P+八
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 = = = + = + = − = +
2M X V+U(xD I=m2m(m2+mN),(元,x)=①(x,x) 2 h 2Mr Vx2+U(xD)Φ(元,X) 一 Er(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 oO,X=y(xo(r) 人h2”+(天(x)=EV(x) 九 Vx(X)=(En-E)小(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 V2+U()v(元=Ev() y(x)=R(r)Ym(O,) x(r)(e, g) x+n2(E-O()-(+1xz=0 x>O,->0;F->∞ x
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