Download - 4-3 带电粒子在磁场中的运动
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4-3 带电粒子在磁场中的运动 经典情形
e
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带电粒子在电磁场中运动的哈氏量
Hi
AB
t
A
cE
qAc
qPH
t
1
)ˆˆ(2
1 2
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几率流
请注意磁势部分
Ac
qppj
jt
*]*)ˆ(ˆ*[2
1
*
0
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Bohm-Aharanov 效应 局域磁场引起的干涉( 1956 理论; 1962
实验)
eB
O
F
G
D
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xldpi
iEt
Nex
E
extx
xBwhen
EH
Ac
qPH
/
0
002
2
/0
2
)(
2
)(),(
)(0
)ˆ(2
1
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某处 B 不为零
x
ldAc
iq
Mex
xAc
iq
xxx
xExAc
iq
A
)(
0)()(
)()()(
)()()(2
0
0
22
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一般解
2/
),(2
)(
pE
Netxx
ldAc
qp
iiEt
![Page 8: 4-3 带电粒子在磁场中的运动](https://reader033.vdocuments.net/reader033/viewer/2022061404/56815232550346895dc078d0/html5/thumbnails/8.jpg)
干涉
)(
),(),(),(
),(
),(
)/()/(/
)/(/
)/(/
OGDOFD
OGD
OFD
ldcAqpildcAqpiiEt
OGOF
ldcAqpiiEt
OG
ldcAqpiiEt
OF
eeNe
tDtDtD
NetD
NetD
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观测点粒子几率
ldcAqp
ee
tDtDP
DGOOFDOGDOFD
ldcAqpildcAqpiOGDOFD
/
/)(/)(
cos22
~
),(~),(2
)/(/)/(
2
![Page 10: 4-3 带电粒子在磁场中的运动](https://reader033.vdocuments.net/reader033/viewer/2022061404/56815232550346895dc078d0/html5/thumbnails/10.jpg)
SdB
L
d
c
q
ldkc
q
ldpldAc
q
2
1
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02
,0
0,0
0max
c
q
d
LB
B
atimum
![Page 12: 4-3 带电粒子在磁场中的运动](https://reader033.vdocuments.net/reader033/viewer/2022061404/56815232550346895dc078d0/html5/thumbnails/12.jpg)
B
O
G
F
D
B=0
B>0
ξ
L
d
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朗道能级 (1930) 量子带电粒子在均匀稳定磁场中运动 有何特点?
e
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稳定均匀磁场的势
))(0,0,(
)(2
1
),0,0(
0,0
gaugecansymmetriByA
gaugesymmetricrBA
BB
AB
BB jxt i
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用不对称规范势
)(),,(
}ˆ,ˆ,{
]ˆˆ)ˆ[(2
1
)(
222
31 yezyx
ppH
CSCO
ppyc
qBpH
zpxpi
zx
zyx
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20
2
232
02
2
22
)(2
)(
)()2
()()(2
)(
2
yyyV
c
Bq
yp
Eyyydy
yd
c
c
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cBq
yyHey
np
EE
nyy
cnp
/
))((~)(
)2/1(2
02/)(
23
,
20
2
3
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...2,1,0
)]/)(/[(
),,(
1
)/)(2/(/)(,,
2131
13
n
qBcpycBqH
eezyx
n
qBcpycBqzpxpipnp
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一般解
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两个守恒量
0]ˆ,ˆ[
ˆ/ˆˆ
/ˆˆ
00
0
0
qB
cixy
xqBpcx
qBpcy
y
x
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分立能级 简并度
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Zeeman 效应 (1896) 原子在均匀稳定弱磁场中
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H0 --- 形成原子的哈氏量
)(ˆ2
1
ˆ2
)(8
)()ˆ(2
1
)0,2/,2/(2
1
20
222
22
0
2
rVpH
Lc
eByx
c
BeH
xVAc
epH
BxByxBA
z
![Page 24: 4-3 带电粒子在磁场中的运动](https://reader033.vdocuments.net/reader033/viewer/2022061404/56815232550346895dc078d0/html5/thumbnails/24.jpg)
略去小项
z
zeff
z
Lc
eBrVP
Lc
eBHH
LabinGaussB
Ba
c
BeL
c
eB
c
yxBe
ˆ2
)(ˆ2
1
ˆ2
)(10
110442
/8
)(
2
0
5
102
2
2222
![Page 25: 4-3 带电粒子在磁场中的运动](https://reader033.vdocuments.net/reader033/viewer/2022061404/56815232550346895dc078d0/html5/thumbnails/25.jpg)
CSCO
frequenceLarmorcBe
fieldmagneticwithoutatomofenergyE
mEmc
eBEE
YrR
LLH
L
nl
Lnlnlnlm
lmnlnlm
zeff
2/
2
),()(
}ˆ,ˆ,{ 2
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能级分裂和光谱线劈裂
p
s