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 ( )2+qg 1 O4 c Ot B=√×A inoy= Ayp
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 a1+V.j=0 尸=Y* 7=1严*+()*甲-中*甲 2 uc ■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)
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
( 1)2 when B (Vs) y(,t=yo(se z/力 √2v 2∠ o(米)=NJnd/1
= − = = = = = − − 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 ( A)O=EyOO v(x)=v0(X)d(元) (V-A)d(x)=0 p(x)=Me ho G
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
般解 r(, t)=Ne h i(p+ ardi iet i E=P/2u
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)d YoR (D,t)=Ne OFD OG(P+q/ c)dI -iEt/h+i( OG D (D, t)=yoR (D, t)+yoG ( D, t) Ne-iEtth (p+gA/c)'dl (p+ga/c)' dl JOFD e OGD
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, t)Y(D,t (p+gA/c)d!/h (P+gA/c) dl OFD e OGD 2+2 cosS )/h )/h OFD OGD OFD DGO P+qA/c) dl
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
4·dl+ φ+k.a 乡y Φ=「B.as
B dS L d c q k dl c q A dl p dl c q = + = + = = + 2 1
