LB#? $ J8 x <!1D>8 z <! N m! a $:0M KE 2KE C3!E $ $K$4@%"&'( I )*K+;,-.
! N M $ E/5 v !K$E 2 h $67J9F =
E$9FKAG, ? $ 9FH EK0I !KOPQ Æ RSTUHE C,-VWQ$TXYZ,9F[
9FH!K E xz \]YZ,!^_`abc,- def/5 g
12OOOO2Oz㻌z㻌O㻌O㻌㻌x㻌h㻌x㻌㻌h㻌į㻌2a㻌㻌I.

㹋㻌v?

?

12E $g$K$4@%"&'( I hi 
E$j/5 v  Æ $kl,-mSnhK$4@%"&'( I o(2)-p E9F,-0Iq,H$!K$TXYZ$QTZlr* nh(3)
K$4@%"&'( I o -p !VWQ$TXYZ,$K$TUQ Æ ! Æ  Æ ,- (1)

O0sin

001

II.

$ Dl k!<A   $$ E 2$ E C3!$ $ Nbc$$ $B$C
! N m! a $: 0M KISK$ $CC3$K1D28?,!+; =$$mg$  l  k  ? $ !$$ K xz \]TZ =$  8$=,!U03$8AG, K$d
$: x z ^_`abc,- OO

2=+3( , )zO㻌

xl+yθ
2a㻌

ϕ(x,z)㻌

?

3$ K$1D8Q!UU   ' ,!$ $ mgl y y K$d$: x z  a!l!y!!' ok-=ma(5) $K$d $4@%"&'( $K$  
7$% %' 'r* nh!m!a!l!y!g!k!!'!y!!'o R,!y!!' !UU$;4VJ
(4)+(=+( , )+ )23____

2__

III.

? $$ KVWTZ,- >9 i$!$ $=!$K$TUQ6*-W *!VWN$<$bc% %' '<$  3L=m

1

21223



1y_ 2 + l2 _2 + a2 '_ 2 + al_'_ + g l + y2l2 + a12a'2

 1  mg 2k y+2k

$% %' 'o !$ $=!y $CTZ $TZ$QTZlr* (7) $% %''o -!  ' $YZDONVJD,-r*  ' B !t
(8) WL (7) r*ONVJD$n!
A !t$7$4=QTZl ! A-r* (9) ? WL (8) r* $4=QTZl$ K4=TZ,- $!xz \]$YZ$F?,p$ (8) r*B$4=TZ -!xz \]$YZ$F? M?= (6)

=

3

1

3

3os(+ )

=os(+ )

7;oMG()4

7;oMG
LB#<$%" ()5

LB 2!
DE$%$M;@ I  M;$290A " e :%e$C#I M;&'$()*+&,<>$-1.F/ 34
56G$ >478:J2 / :57%$(= ?HK NO//2PD$QRST&7/UN <VWXY $Z[M;!\] M  " e )^ $*+&<_`
E B ab&cdZef rg v 1.F7 2h%)i2  j&7ef r klef a Umni2 )o6$pq
r7stu1.F v&w 90$xy
100 MeV

8 eV= 10= 1 6  10

1 eV = 1 V = 1.6  10

19 C

19 J.

+1BrM, +e^(1)(2)

1

1.F$6z T ) v r {&7/ |wNO}x (1) ~{ (3) U.FuS/ /:%~{5%U *$6z.F / )~ klef r=a

N$.F% K  eBaM 47w

apq$6G f ={ M;$.F% K  C#  M;$\]
 :M7UNK (3) B = 1.6 T= 1.0 meV

28= 3 0  10 m/s

2 = 9.4 102 MeV[T℄ =2[Vs/m ℄(4)

!/$}xO7 uxS/$}xv~$\] % hNj$K:.F% %~{,%7Nj$$/}x (1) N6z T $M v~$\]H~ $UU:¡r%~{5%UmnM;2 .F%)26i2 rM;$v~$\]ji2 N<>)*&{6z T)J2UNM; r Is F$6z T .F%)1.Fgw N/$ef$<_`E B  r Is$ G&&{&7~ y
1.0 10

2 MeV= 0= 02II.

$1Z*+&<_`E B
H@gw ?H9 ef a^ $&Cd@)*$E?=MNc9&<6$ <7 <6$43 def a N I E?$[$Dg lC$Nda &w<6$4 E?0$4$<$O=$&7 Au&> 9  N I :E?$Z[ <6$4<>)H@ )<6$4$<_`E B 
N7E$<  $< UN<>4J2&7j$ = 1.0 m= 1.6 T2

0 =1.6 T

4 10

7 Tm/Ad

B
Ia

C

^2

B

E
B

Ab

B
B//

H

B
B//

Fb

G

D
C

B'

B

B'
B'
B'//

B'//

C

^
(5)

F

B

B'

G

3

7¡^ $~{E?< )< > dab&<_`E$ B? E?Z[ B?0 dc9&<>
3(7)E?Z[ H 0 '$&>7):¡r~9 NOB  H B0 H 0 K UNE? NN7&7j$
E?$d4$H}&bJB
9 //ddc9 ^ $ B c9 :bÆ0bÆ
/$bJB47B? B? :¡r>7!,<>r7$ %$K~{F
H== (=== )0=

ABCDEFGH

BC(ABCD==3

AB = AD =AE =)(6) H==

0H==:¡r>7$K~{F^ $6 C !Dg l d w $<> H $ @ H H dl $C
N I U }x (5) $>747= l=d $>7$B
H@gw NIM& I #yNOd
III 8&lgjr <$c9&1 <6$ <7<6[$<$O=$N<_`E *+&{&7/$> $< $+;9;
(8) ^ $ xy z !NO E<64N0$-?  y y ! $E r79 <_`E$ z  B y ^^$ y ! CD /$ E $H $$K~{ B =z $9{
(7)

2+C



0 

=

= 1.6 T
0.10 m.

40z

A04AyzAyx BBz0^(9)y4

@~{E  z  B& /$/ }x (8) $234z d$ B $9)'J2 ~ < )E Is^ ^$6) / Lw
A= 0A(y = 0= 0)

y48

(10)

^ ^$6)hN< $$M;$.F9 z dZ ^ $&1.F)2GK //M;) z dc9& z > $dZstu1.F > 9 /$M; z dL )F/ ^ w &Ty04;^ I</$M;$ E .F$8!x $@K M;F $%g{ $ $ y  z |wNO EJ$NM;$5) yz d E$*rK 
4= 01= 00= 05

A'A'zxy^

59LB#% $;NN8M<5G$;!@<>C: 1F$7  2E<>$ !6$K 2E<>  $"&'&!()4A0$6N8M<5G"@<>*!2E<>3?F+ ,-.!N<5G"<>*/9D!=<56HIJ(MRI) OPQROST SUVWU% 6J XYVZJ$[ \UW]W^_`
I. %  1/2 ab S = (Sx ; Sy ; Sz ) c z de8Mfghijk$SUWlm_` no= h2 j"i h#j + j#i h"jih Sy =j"ih#j+j#ih"j2h Sz =j"ih"jj#ih#j
2

Sxj"i!j#i  Sz 8Mpq +h=2(1)h=2 8Mijkrs

lmrDt j"ix!j#ix q Sx 8Mijkrs $uoj"ix = p1 j"i + j#i2
1j#ix = p j"i j#i2

II. vwx yz{ |Ir}F~+ j(t)i 4k H $SUW ZrnVihdj(t)i = H j(t)idt
te iHt=h(*)

k H q4$OU>! () j(t)i lm_` ()ijk j(t = 0)i 4ab
rsoj(t)i = e iHt=h j(t = 0)i $SUW!z Z$UQO@<> B = (0; 0; B ) C V[% 1F$]r B 4 _OUD+rs[% <5G$ !k H  H = ! Sz rV!! = eB =me !e [ (e > 0)!me [! rs
0000(2)000

 t = 0 r% q x Z$UWU() j(t = 0)i = j"ix $]
() t r}F~+ j(t)i $ j"i j#i  ¡¢r£¤10(3).

III7$8EOr] !% q3?F+ ! r z <&$: 1F qeOr$8EO B12 q=M $u.!
Sx !Sy !Sz  j(t)i Bp$5._
0_` !Q@<> B W xy JLF$3?F+ ! r2E<>$¤0

B = (B1 os(!t); B1 sin(!t); B0 )k H !lm_` 4 ,-de V q= H0 + V= !0 S zeB1
V =fSx os(!t) + Sy sin(!t)gm

HH0ekr4() j(t)i $]
(4)

 t }F~+ j(t)i  j"i j#i  ¡¢r£¤37+4,@` H _4,-@$eN!
0j(t)i = +(t)e iH0 t=h j"i + (t)e iH0 t=h j#i

3 (t)! (t) 37+rs (*) $SU+ind + (t) i!0 t=2d (t) i!0 t=2
ej"i+iej#i=dtdt
2= eB1 =me

O $uors(5) 37+ ! qKijk$OUHeZ$5._
+lm> (6) (7) r!2E<>3?F+q@<> _% : 1F
3?F+ C>!O!! = ! >$]
0= 0 r() ji % q z Z$UWU  (j(t = 0)i = j#i)
() t r}F~+ j(t)i $ j"i j#i  ¡¢r£¤(7) () j(t)i \UW%  z dep hSz i $5._
(6) thh G ii
V _W hSz i q> (7)  _`O4$ U` !A :S_W H0 8M() (j"i ; j#i) 4A0q0VWU U` $ WU
> (5) HeZ$> 2 !_`OA0q !  !0¤rs qeN 8MO<5G @<> r6qKV ^2E<>! ?F<>r_U 4r 4q!% 6JrSVrs
11o(t)e i!t ei!0 t=2 j"i + + (t)ei!t e i!0 t=2 j#i

(7bSMG)12

(7bSMG)# % 13

LB#. % !54$E2KDCGKDE20=CG0=I G54 % !54$FG8% !54NF @< % !M "&>'( )*+,-./1
(1)? 1 12 3% !54 CC &9/  " 6I( ;7& W ( % !54 CC :28 AH( GJ$O"P" Q 
Q Q28RS( GJ$O"P" Q Q  ? 1 TU% !
54&V WXYTU% !54Z[54&9\( 1]% !54 CC N
000121020

=10=1Q2Q1Q02
Q01

EW G^_` 2 abcdedfgMh( ij
浧䂸䄟44&::&44⇝䂸䄟?114

II. A- I 72

Q =Q = T =T WX:28Q28@B2E&O"P"T T 5( % !54N$
1

2

12

12



= QW = 1
1Q2
Q1=1T2T1

 $ " TU6G>% !=M@< "?&2* ! 5
;$" 1 X )$!&; >% !
! "&M( )*!% !54&1W)
% !54 N0WX+,-./1(2)GJ CW ?&62 T 2E T 2*)O IM GJ Q &*1)GJHJ ÆQ ?2HJ ÆT 4&*1)WCW  T $T( 00% !54 ! RG&; X?&2*)
( ;7 W ?&2* IM GJ Q 43X9/X1(3)? 2 162& T ?2& T WX! #H;7 ÆW&W)! ?RS " GJ& ÆQ6 !
AH( GJ& ÆQ W) ÆW=ÆQ & T  T &X $j00(4)0- (2)  (3) 72&X?2 T ?& T 2* IM ;7W & T T CW &X $j00㻃䂸 7ˡ4ˡ:+ˡ4 R⮥㺦䂸 7R?215(5)!@ ? ! Q=W &*1

(6) T > T0(7) & T 4?WXO37&%cI$

62 T ?2 T 2E:&B W)  $(a)   (b) J$ ( ) B   CWY59&.0;5Fj1
0(8)W) log(T =T ) &HJ (T =T )  2
6WX- (5) *) 6<&*1(9)62 T = 290 K (L 17 )?2 T = 340 K (L 67 )  - (8) *)6<&; X &*1

(10)T =T0  1 T = TT0000

$!$ 54 9/X )8 !
$ 54 O>[ $- (5) *) H XOB! OMM6./1
4$  54!% !54Z[54cdedf
gM&EWX9\j116