Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7...

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Transcript of Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7...

Page 1: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

.2 1 4

. 1 -101 0.@::

401: . @. .11 .4 . 3@ 4 3:6 0.4 . 5::

Page 2: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

). .

.. . .: . :. .

(. / . . ./ :. . . :.

Page 3: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

& , 2.

11 . 2 1 12 2, 2 1

Page 4: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

-,

) - )) - - -- )) - ) , - - - - ) -

, ) - ) -- ) - )

C ) - )) - , - ) ) -

) - - )- ) - - ) - ) - - ) , -, - ,

- ) - - ) - - ) E - ) - , -

- ) - ) - - (- )- - ) - - , ) - )

) - ) - - ) -) - )

- ) - ) )

Page 5: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

,,

, ,

,

Page 6: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

:H M 84. HMAKH=M IH= MAG IB H M . AHM GAMAK K=G A IH84

6 80 K=M I

84 846= HAM I A

=K A G) , ) ,

6= HAM GIGAHMG

SG ) )

G= HAM =M IH 6T4U

9G

2= ) ) ) )/ -

6= HAM BAH M 1

9 2= ) )

6= HAM B 6VW

, ,

6= HAM B A 3 0 G 7A ) (/ - ) (

6= HAMA M O M

3 G ) )

6= HAMAKGA= M

3 G ) )

= G AKGA= M/ )

3 G /

Page 7: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

tc

tcc

¶¶

-=

¶¶

+=

==

BE

DiH

BD

1rot

14rot

0div4div

p

pr

t

t

¶¶

-=

¶¶

+=

==

BE

DiH

BD

rot

rot

0divdiv r

ò´

=

==

=

=

+=+=

3

221

0

221

0

0

0

d4

,4141

rI

mqrmmF

rqqF

rsH

HFEF

MHBPED

p

pe

µe

ò´

=

==

=

=

+=+=

3

221

221

,

44

rd

cI

mqrmmF

rqqF

rsH

HFEF

MHBPEDpp

Page 8: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

E = 1 4 =

-1 1 4 =

G = 1 4 =

÷øö

çèæ ´

= ò 3dr

CIm srF

( )EF qrqqCF e == 221

( )HF mrmmCF m == 221

0 .= = 11

/ G) ) I

)

1 EC)))

= 1ECG

)) I

)-1

1 CG) I

))

( /1 1= 1B

Page 9: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

/

- : A : : M 2.21 N 2,

- : 7 ,M2

M 21 2. 2. N2,

221

041

rmmF

pµ=

ò´

= 3d

4 rI rsHp

HF m=

rIIF 210

2pµ

=

)1 A HA A 7 A 7 7

A A P ( 2. 1 7

]m[1]A[1

2]m[]N[102

2207

=´ -

]m[]H[

]A[]N[104 2

70 =´= -pµ

0 A= A

Page 10: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

1 B G 8 NA B G 8 BF G O

8 F3 / FF

50A 6

EG A B G 8 ( 3 P6 ( A

8GE A B G

5 8M( 3E B EM 3

M 1 A( 6

M ) 1 A6

4 EA B BGA B G2 .

5 I E 3 M3

M 1 AM 6

5 E8 B 8GB

8GE A B GM ( 3

G M 1 A

M ( 6

Page 11: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

39 @ F9 @

9 9C

709 CC8

51768

/ G2

(

. (

4 ()) MHB

MHBp

µ4:

: 0

+=+=

cgsSI

Page 12: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

[ ] [ ] ( )22

2

0

52

2

2

2

1041N10dyn1

11

-

- ==== SImrm

90104 -= pµSIm ( ) [ ]Wb

10104104 08162 µpp =´== --

[ ]Wb10

]cgs[ 0µ=����

[ ] [ ] [ ] ( ) ( )22

0

0

022

20

0

5

1010

41

101010

41N10Oe11dyn1

--

-÷øö

çèæ

´÷øö

çèæ=

÷øö

çèæ

==´=

µ

pµµ

µ

pµ pµ

410

10

30 ´÷øö

çèæ=

[ ] [ ]A/m410Oe1

3

HB 0µ=

[ ] [ ]T10410104

410Gauss1 4

37

3

0-- =´´=®

pp

HF m=

Page 13: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

0

.= 0 0 . 1 0 / 0 /=.0/ 0 /. .= 0 ( 0 = 0 1 = 0 0 0) = = .

Page 14: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

. . : 2 2 2 . : . . 2 : ..:2 :2 : . 2 2 : :. 2: : . . .:2,

2. : . . 2 , :. : . .:2, 2. : : . . .: . 2

: :. .:2 :2 2

Page 15: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

-

--

--

--

--

- - - - - .-- - - - -

- - - -

Page 16: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

1, 1

1 1 1

eμ ml=

rq

m-lm

μ

( )53

3rrrμrμH ×

+-=

( )53 2

32 rc

evarc

eva rereH ×÷øö

çèæ -+÷

øö

çèæ --=

-e

r

ve

. .1 :e

. 1. μ

eμ ÷øö

çèæ -=

ceva2

Pemcemva

mce

22-=-= lBµ-=

[ ] [ ]÷øö

çèæ ×úû

ùêëé´== - mWb

2Oeerg,emu10927.0

2020

me

mce

B!! µµ

1

vaP m´=

1 1

[ ]mWb10165.1 29 ×´= -

lmce2!

-=

lP !=

Page 17: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

l!.

. .

, , . , . ,

lμ Bl µ-=

. s! ( )2=-= gg sμ Bs µg

Page 18: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

F @ 3

.@2BC@2B 2 B: 2B: ) ( 0 13 /2BB: B2 B) ( @ B2 B@C BC@ ) 3

,2 C@2B B9 2 B: B 2 :@ 2B :

B9 C 3 @ :@ 2B :

Page 19: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

C /82

,2 . . 282 : .:1 .: 282 : 6: . 2. :2 6 2: 3 F 6: 3 22 . 2.8 8. 2 .:B 282 : 2 ,2 . 2. 2 2 . :2 6

2: 6: / 8 ,2

: ,2) (F .

282 : ) F

(F 282 : .

Page 20: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

1 .

( )rVm

H +Ñ-= 22

2!

( ) ( )rr eff =H

. 1

( ) ( ) ( )jqf ,YrR=r

úû

ùêë

鶶

+÷øö

çèæ

¶¶

¶¶

-= 2

2

22

sin1sin

sin1

jqqq

qql2

2

2

22 2

rrrrl

-¶¶

+¶¶

1 . 1 1

2 . 1

. 1 1

Page 21: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

jqjq immlml

ml ePCY )(cos),( ,= ( ) jq

pimm

lmm eP

mlmll )(cos)!()!(

212

211

2/12/)(

úúû

ù

êêë

é

+-+

-= +

( ) ( ) ( )rRrRrVmrdr

drdr

dm

el=ú

û

ùêë

é++÷÷

ø

öççè

æ+- 2

2

2

22

22

2!!

( ) ( )jqljq ,,2 YY =l

( ) ( )jqµjq ,, YYlz =

( ) mll =+= µl ,1( ) ( )jqjq ,, mlYY =

( ) ( ) ( )jqjq ,1,2 ml

ml YllY +=l

( ) ( )jqjqj

,, ml

ml mYYi =

¶¶

-

( )jq ,mlY

( ) ( )jqljqjqq

qqq

,,sin1sin

sin1

2

2

2 YY -=úû

ùêë

鶶

+÷øö

çèæ

¶¶

¶¶

( )jq ,Y 2l

[ ] 0,2 =zll ( )jq ,Y zl

)(xPml

!,2,1,0=l

llllm -+--= ,1,1, !

Page 22: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

),()()( jqf mlnlnlm YrRr =

!"

3,2,1,2 22

4

=-= nn

mene

01 E-=e

40

2E

-=e

90

3E

-=e

160

4E

-=e

0=¥e

)2(1

)8(4)18(9

)32(16ne

20

nE

-=

( )]eV[6.13],Ry[1

]J[42

,2 2

02

4

2

4

0

=

÷÷ø

öççè

æ=

pe!!memeE

( ) ( ) ( ) ( )rRrRrVmrll

drd

rdrd

me=ú

û

ùêë

é+

++÷÷ø

öççè

æ+- 2

2

2

22

212

2!!

( )rZerV

2

-= )()( rRrR nl= !"

3,2,1,2 22

4

=-= nn

Zmene

������� ���

Page 23: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

. ..

.

. .. .

Page 24: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

lm

0 �1 �2 �3

s 0 ― ― ―

p 1 ― ―

d 2 ―

f 3

p21

qpcos3

21 q

pj sin23

21 ie!

qp

j 22 sin215

41 ie±qq

pj sincos215

21 ie!)1cos3(5

41 2 -q

p

qp

j 33 sin3581 ie±!qq

pj 22 sincos2105

41 ie±qq

pj sin)1cos5(21

81 2 -ie!)cos3cos5(7

41 3 qq

p-

jqjq immlml

ml ePCY )(cos),( ,=

( ) jq imml

mm ePmlmll )(cos)!()!(

212

211

2/12/)(

úúû

ù

êêë

é

+-+

-= +

Page 25: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

n l

1s 1 0

2s 2 0

2p 2 1

3s 3 0

3p 3 1

3d 3 2

4s 4 0

4p 4 1

4d 4 2

4f 4 3

( ) ( ) 2/2/3

020 2

221 xex

aZxR --÷÷ø

öççè

æ=

( ) xeaZxR -÷÷ø

öççè

æ=

2/3

010 2

( ) 2/2/3

021 62

1 xxeaZxR -÷÷ø

öççè

æ=

( ) ( ) 3/22/3

030 27182

3811 xexx

aZxR -+-÷÷ø

öççè

æ=

( ) ( ) 3/2/3

031 6

6814 xexx

aZxR --÷÷ø

öççè

æ=

( ) 3/22/3

032 3081

4 xexaZxR -÷÷ø

öççè

æ=

( ) ( ) 4/232/3

040 19211424

7681 xexxx

aZxR -+-+-÷÷ø

öççè

æ=

( ) ( ) 4/22/3

041 8020

152561 xexxx

aZxR -+-÷÷ø

öççè

æ=

( ) ( ) 4/22/3

042 12

57681 xexx

aZxR --÷÷ø

öççè

æ=

( ) 4/32/3

043 35768

1 xexaZxR -÷÷ø

öççè

æ=

( ) 2200 /,/ meaaZrxxRnl !==

][10529.04 102

20

0 mme

a -´==!pe

���� �����0a

Page 26: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

)3(1165)1cos3(

165)( 22

32

320 rzr

r -=-®p

qp

f

yzr

rri

r 2*

3213213211

415sincossin

415))()((

21)(

pjqq

pfff =®-=-

zxr

rrr 2*

3213213211

415coscossin

415))()((

21)(

pjqq

pfff =®+=+

)(116152cossin

1615))()((

21)( 22

22*

322322322 yxr

rrr -=®+=+ pjq

pfff

xyr

rri

r 22*

3223223221

16152sinsin

1615))()((

21)(

pjq

pfff =®-=-

223 rz -

zx yz

xy 22 yx -

Page 27: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

)5(1167)coscos5(

167)( 23

23

430 zrzr

r -=-®p

qqp

f

)5(13221cos)1cos5(sin

3221)( 22

32

431 rzxr

r -=-®+ pjqq

pf

)5(13221sin)1cos5(sin

3221)( 22

32

431 rzyr

r -=-®- pjqq

pf

)(1161062coscossin

16106)( 22

32

432 yxzr

r -=®+ pjqq

pf

)2(1161062sincossin

16106)( 3

2432 xyz

rr

pjqq

pf =®-

)3(132353cossin

3235)( 23

33

433 xyxr

r -=®+ pjq

pf

)3(132353sinsin

3235)( 32

33

433 yyxr

r -=®- pjq

pf

225 rz -

( )225 rzx -( )225 rzy -

( )22 yxz - xyz

yxx 23 3- 323 yyx -

Page 28: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

1 1 1

1 .

11

Page 29: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

+ A 1 1 1 3

: 3 3 A 1 A 1 1 1 2 1 2 A :

mln ( 3 1: 1 2 I A :: .

( 1G 1: 1 2 I A( 1 3 1 2 ( llll -+-- ,1,,1, !

!"

3,2,1,2 22

42

=-= nnmeZ

ne

1 1 3 2 0

, 31A 1 A E 1 : 3 A: 3 A 1 1 1 3 3: A

l: :A 1

) 13 3 0

: 3 A 1 1 1 3 3: A ) 13 3A : 3

Page 30: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

- ) , ) .

.) ( ( . ( . - ) , ( . .. . )

( ( . )

nle

å> -

=ji ji

CoulombeHrr

2

( )122 +l

. ( . (

. ( . . ( . . - . ,) . ,

åå ==i

ii

i sSlL , . ..

Page 31: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

( 2 2 02D 0 0 : : 1D

0 0 :1 02D ( )( )1212 ++ SLSL,

. 0 0 2 2 0 .H . :

D 2 1 C . :( :1 0

0 . : C: 20

, 0 . : H LS 12 + L N . - )

Page 32: Magnetism-1-1 - 北海道大学phys.sci.hokudai.ac.jp/.../lecture/pdf/Magnetism-1-1.pdf1 16 7 (5coscos) 16 7 32 2 3 430 zzr r r® -= - p qq p f (5) 1 32 21 sin(5cos1)cos 32 21 22 3

Hund’s rule C .,

. , ,

(, . ,

, , , ,

, , , ,. . ,, . ,. ), . ,

,. 1 A . . , 2 ,.