2.1.2 The solution---separation of variables SubstituteΨc,0,Φ)=R(ro(o)Φ(φ)into the equation 1 ay8πm(E+ r2 or r2sine 00 00 r2sin20062 h2 Zew=0 4π8' 2 and multiply with R(r)⊙(0)Φ() 1 oR) 1 + oΦ(@8元m(E+ R(r)or or ⊙(0)sin0a (sin) a0Φ()sin20ap2 h2 er2=0 π' 1 (r2R( 8mle(E+4π ze2 )r2=[ 1 (sin 1 a2Φ(φ) )+ R(r)ar (e)sine a0 ae Φ(p)sin20ap2 2.1.2 The solution --- separation of variables Substitute r, R r into the equation 2 2 2 2 2 2 22 2 2 0 11 1 8 ( ) (sin ) ( ) 0 sin sin 4 m e Ze r E rr r r r h r and multiply with ( ) ( ) ( ) 2 R r r ) 0 4 ( ( ) 8 ( )sin 1 ) ( ) (sin ( )sin 1 ) ( ) ( ( ) 1 2 0 2 2 2 2 2 2 2 r r ze E h m r R r r R r r e ] ( ) ( )sin 1 ) ( ) (sin ( )sin 1 ) [ 4 ( 8 ) ( ) ( ( ) 1 2 2 2 2 0 2 2 2 2 r r ze E h m r R r r R r r e