4-3带电粒子在磁场中的运动 ■经典情形
4-3带电粒子在磁场中的运动 ◼ 经典情形 e
带电粒子在电磁场中运动的哈 氏量 H=2μ q )2+qy E=-1o Ot B=V×A 边=FI
带电粒子在电磁场中运动的哈 氏量 = = − = − = − + i H B A t A c E A q c q H P t 1 ) ˆ ˆ ( 2 1 2
几率流 a,p+V·j=0 p=* j=平*p+(H)*y ^ 乎*A C ■请注意磁势部分
几率流 ◼ 请注意磁势部分 = + − = + = A c q j p p j t )* ] * ˆ ( ˆ [ * 2 1 * 0
Bohm- Aharonov效应 局域磁场引起的干涉(1956理论;1962 实验) F e● 口B
Bohm-Aharanov效应 ◼ 局域磁场引起的干涉（1956理论；1962 实验） e B O F G D
(D Ay=ey vheB=O(V米 y(x,t)=yo(e eye yo()=/e
= − = = = = = − − x i p dl iEt x Ne E x t x e when B x H E A c q H P / 0 0 0 2 2 / 0 2 ( ) 2 ( , ) ( ) 0 ( ) ) ˆ ( 2 1
某处B不为零 A≠0 )yO=Ey( 力C v(x)=v0(x)( q A)(x)=0 文)=M一Jn
某处B不为零 = − = = − − = x A dl c i q x Me A x c iq x x x A x E x c iq A ( ) ( ) ( ) 0 ( ) ( ) ( ) ( ) ( ) ( ) 2 0 0 2 2
坟解 y(r, t)=Ne h hf(+rdi iet i E=p2/2
一般解 / 2 ( , ) 2 ( ) E p x t N e x A dl c q p iEt i = = + + −
干涉 -iEt/h+计(p+qA/c),dl VOF(D, t)=Ne OFD iEt/h+i (p+qA/c)di yoG (D, t=Ne OGD P(D, t)=Vor (D, t)+yoG D,t) Ne - i e JoED(+gAlc)dl (p+qA/c)'d tenD
干涉 ( ) ( , ) ( , ) ( , ) ( , ) ( , ) ( / ) ( / ) / / ( / ) / ( / ) + = = + = = + + − − + + − + + OFD OGD OGD OFD i p qA c dl i p qA c dl iEt O F O G iEt i p qA c dl O G iEt i p qA c dl O F N e e e D t D t D t D t N e D t N e
观测点粒子几率 P(D,)~(OD)2 i(p+gA/c) dl/h JOFD +e0(b+g/c) =2+2c0s6 δ=( )/h=(+)/n OFD OGD OFD 丿DGO +9a/c
观测点粒子几率 (p qA c) dl e e P D t D t OFD OGD OFD DGO i p qA c dl i p qA c dl OFD OGD = + = − = + = + + + + / ( )/ ( )/ 2 2cos ~ ( , ) ~ ( , ) 2 ( / ) / ( / ) 2
.a+ ·dl (D +中k·dl qΦ,d2x4 h+乙元 Φ=|B·dS
B dS L d c q k dl c q A dl p dl c q = + = + = = + 2 1