 Ì$`oU`oqÁÏÃn_oanM[nQÍF7KQÎ_o(`o¸/µ(+-Ðo/uX¨Ãn_o³

+·emÇh(Ð´,+À¦/$0*½*ÏWÏo"}/«|++Ð

 



19  20 QªÏan¶M[n¶£§Ï_o+Ãn_oµ(Ï¹¥oË»,(+SÄ¤VmkÉºÐ, 19 Qª$,#R
 I. >HN=L



.



Ð

/p¯goo·aÍAIL5?1Î/Z 1687 v+ÐJ.C. E7934J¦w/t

-E7934J

/p 1864 v+.,+Ðp+]Ç&ÏJ.W. 6@:Í1876 vb! 1878 vÎ' H.L.F.v. BJGCJ<Í1882 vÎ(i(ly~/d®+xTP(),Ð(Ï´+Q,/Â+j^Í



Îµ

)

,

,Ð
 OÏÅ­±È©nÍrÈnÎÆ$*+ 1897 vÏ19 Qª&¬.*¼ÊÐ{¾+¿*an´ 1911 v*Ï L.E. DJ<EL(*p

ÊÎÏan¶&£§ 20 Qª\%/z,)

Í1887 vÐ(Ï19 QªÏ´+Qµ¬.*Ï´Q¢)Ï+Ð

ÏA. 12L8H;2L/² 1905 vÍ¡s¶Î 1916 vÍO°¡s¶Î+Ð¡s¶&cYof%+RlÐ!%
?

/

14026
A



 <9!(~z!;®19 :!dH-,¯!(Z«u!;¯?!w.n©),+¯A.{§®JW!AB,n©.|Ct'!.

 r'I14026"xJW!SM

"!



g

¯

e),¯14026"\o!

&¬I8{§!A­ )*®LªR"®,)!{§" 656.5 nm®486.3
nm®434.2 nm®410.3 nm ¯!u.%p+jF!" J.J. 3657¬1885 ]­¯b"14026!{§¬λ­⎛1
1⎞
1= RH⎜ 2 − 2 ⎟
⎝2
n ⎠
λ

(4.1.1)p,+.¯ RH " 109678 cm-1 V"q¥Yo+, n = 3®4®5®6-+¬



.l®Q­¯@!{§",[g+¯d ®n = 7¬397.1 nm­ ($ n =8¬389.0 nm­A',¯^(4.1.1),+xJW!A1
4026.
 20 :

$¯+^(4.1.1).8G

⎛1 1 ⎞
1= RH⎜ 2 − 2 ⎟
⎝l
n ⎠
λ

`{§(4.1.2),+A14026D

$¬l = 1®1906 ]­®¡UªR!

,¯UªR!

$¬l = 3®1908 ]­®$¬l = 4®1922 ]­+¯3657D"%'+¯,)!
v¤,!"Z«9!P¨.y+!

f&+¯X!£v


l=2

_

k£

+k!aE.K++¯ 14026!p"®,¯^(4.1.2)"®xJW!~i%*®~i>.hN+.,#)

pomY,+.O+¯("¬$$­+sc,+¯-®n mY,+~il mY,+~i!*T-*¬'#­ =}Y!{§!A+®¦+-+¯¢~i.TG+





Z 4.1 «j i+2
0?>!q¶·¸=1;?6?>7!q¶·
9:>5!q¶g·¹+n!A"&.W++¹+P¸,.!(*¦v£¹ ´!D

G.LB"(ª!¢"%/s°¸¤

Pc!A"d[+

§+"&¸G!w),+¹!

!¢"D

+G!yN|Mm

&+¹!(X².xO+'+xD¶µD·.+¹µD¸HjG.fI)¥++¸_¬¸µD+"d[¸p+«j¶{j·.k)HjG"fIVQ¸p&«j¶{j·.µD«j¶µD{j·¹xµD"g¯!&^Y&,¬l¶·

¸D

+¹

VQ,+¤«j.+"µD«j.+T+¹ «j!X²?hp·.

RKe!}yN|{jhp¶38<4'+¸yN|¶ν· k±]yN|,g³E@¡+u),+¹,).

+ab¨ 1900 o¸M. 9:>5"C!q.&
C!±]!­.\'+¹,±],

¶1886 o·($¶1900 o·¶Z 4-1·¹t

p.©S-+®``"IyN|{jrU&,¹1+Jq.z¹i¸~!±]!_F!#.

ρ(ν ) =

hν
8πν 2
3
c exp( hν /kBT ) −1

 h f(4.1.3)2

O)(|a§\|a(uZq(ªT IY

$(¨(ªkB 

C'

 R 

£R

l(



'©X 1

§R = NAkB¨ªb(4.1.3)oKq^£RU

©!oKq[¦w*

G

ª
 _E*d(¢X¥

H*ªE¢

Jw©
 ¢X

H(HEB ¢X

H(#oKq_y"§(¨( D?;EF¢X
i

S

&)ªE*L{('cE$t~](



%'T

)&s

.37/9*<(



ª


(

&(ª A. ,-8152-8 1905 `©E

oKq§ν¨h hν.37/9*mXo()©4680b

IYrz%g&)(>*np© EX*O+ªeoKqνE
X.37/9hνK hν/c *$ª&©EX*)©
E¢Jw©:VWw
¢X

¥

H

¢X

_y"Us)(

*ªEX 1 C.37/9

.37/9v)((©v

.37/9§W¨d(D*Q§_¨<((ª=j)(§P 4.2¨ª v.37/9

O+(ª&©¥H¢XA

.37/9*K.37/9§K¨$(&)(&©K
ª$¤@kN*$ª2
exp(x) ex MkNª b% x ¡   >[;x}ª N 4.2 EKb %FUE]L_Q}L,49-;W @?_,49-;DA=]L_lrkOJ%%',
49-;CSI#

K = hν − W
aY&%[#&T!68:.d(4.1.4)

P

qbm&(hx$h P<u

e\{(o%

&(






&j%

EVg(opQ\{!% neQ^>

tB

!%

&%FUne^>nee"^>(

)+3"% X r^> A.H. 0:63:"$wG

/85

&iz%1923 W
 *+:172+:EKby`]L_νE~Q,49-;hν}L~ hν/c (!

&

cQ

"%E~Q^>(s%}L~CSN 4.3 v



%

FUe(fR i^>e( o MHQ{~ m^>Z|X( VN 4.3 0:63:^>%}L~CS}0nVBov

[1nθ)6|5ULg#

⎛ hν ⎞ 2 ⎛ hν ⎞ 2 ⎛ hν ⎞⎛ hν ⎞(mV ) 2 = ⎜ i ⎟ + ⎜ o ⎟ − 2⎜ i ⎟⎜ o ⎟ cosθ⎝ c ⎠ ⎝ c ⎠⎝ c ⎠⎝ c ⎠=h2 2
ν + ν o2 − 2ν iν o cosθ )
2 ( i
c

=

h2
2
ν − ν o ) + 2ν iν o (1− cosθ )
2 ( i
c

[

]

&}Z<\H=P$h2
ν iν o (1− cosθ )c2

m 2V 2 = 2

(4.1.5)(4.1.6)

#}/]|*,-+.9K

1
mV 2 = h (ν i − ν o )2
l(4.1.7)'&|m(ν i − ν o ) =hν iν o (1− cos θ )c2(4.1.8)

 V )b@&}:q|Z<\|avzλ{wc = νλ

(4.1.9)x8&$|T(4.1.8)av)6Δλ = λo − λi =_hh
(1− cosθ )mc(4.1.10)

&}h|m|c '!^sL\&$|avH=t[1n






R

7K&

(&}

|:tJiKG
A

;'$'&

'Myj`/k}|Z<\X*,-+.r<t)Y}:tJfGF'

&}




 e4)>3cS

d&Wmdt)



zC{

}uQ"CudOtNc2p/L%|E'&?J\zN{D'DI
C = 3R ×N
NA(4.1.11)

[ 4.4 6/BAF;zb+-/F3C5/F}g
6/BAF;yuxf 1000 K,#),
wR

1819 e9CEF=8.



3

VP{}_%sW(L.E. ?D7@F1871 e

U^ 1 mol zb 3R ,zb
.wR

M]

zb

ax

*6/BAF;$>0(6/BAF;
VPO%'d4.4>0#Ji

xfX(

(VPO[#1905 e W.H. <DF4:`QzS_HwR%)!

9CEF=8)!&

cfzb

\Lzb

VP{}_

0 &

}

)

,jZ( A. -/F3C5/F

1907 ezb},~6/BAF;vM]lT,sh&)(

?D7@FXvtIU^mT%'z

mT%`|!,kn+mTp νN")((zb

(1<D2Go)

1<D2G hνqp

S_rw%

2⎛ N ⎞ ⎛ hν ⎞exp( hν /k BT )C = ⎜ ⎟k B⎜⎟
2⎝ N A ⎠ ⎝ k BT ⎠ [exp( hν /k BT ) −1]

9CEF=8. 9CEF=8.KY,

(4.1.12)¼¬/.Ö³tÍyÓT = 0 KÔ!sÅ! 0 .ÖMÕ

1 an- 3Ó

^

^

an

J?*D6°UlÀ!/)£À.

»/.ÖÌ

.R1¥

sÅ

.Ö

¾!mË!]1b(1±Õi!hS¾)q/¾

P. >A5

ÕyVo

¾Ó1912 xÔ

M.Ö

 anK[n¾Ç!+-¨

¤©

O$f

! 20 O®

\(.

.4IC3´PÁ

1½%/"Õt¿0,t¿Ã1)
&2Q+Q/.
n

4IC3´!TR)

C3´

m



Õ

k0.µ,/.Ö{QºQ/Ö4IC3´P

BJE>I}²!Õ
u

4IÎ·1)!0

g'/.¢,/Õ
#
rÑ!Õ
#

1¥Ö'-an¹/0m

!an H:C8L?

)­`an.°!emn+

µ,/ÖH:C8L?

.ÖrÉ!ÕanÎ·!ÏwÐjÊP.1¥.ÖzÕan!În
BJ anE>I[v1½%Ö

+Æ«1ÂÄÕ

rÑ²!Õan

ÕÖ1911 xÕE. H:C8

L?!4IC3´1Æ«ÕQ/



Õ
Ì





¦p¶

,Õ/!z/.¸.).Ö!|

Ul.

sÅ!ÕYÈ,anK[n!N_[Ö



À

»/.ÖrÉÕ=5FE+hSO)7@I9L

 45J;G<5J

m

Ul

!Õ²P

.1f¡zÔ.1µ.ÕÒÈ!sÅ! 3R cZX.Ö=5FEJ?

~^,..ÖÎnm

10-4 W§y.Ö

rÑan

ªd

ÀÅ!°an¹/Õ.Î·1)anÎ¯ 1800 [

1 .

,Õa

S¢R
K?HSph%VXTO)©SN%%

%¯R¢|5]¢|5®fm%¯HSp($%rP)%z'¯ HSp©S¥©tC¬ª©`C­¡C¬1n`C­9
%#&%¯HSp©S¨) r %®ª©`C¡C<

F = –Ar/|r|3a)(4.2.1)

%¯ª©`C A 

e2
ke =
4πε0
2

%¯

(4.2.2)e ©t¢®ε0 ©}%¯ &#8):&%®

Ae = 2.3•10-28 N m-2 %¯0k®¡C®G )¡CXj®m  M )©S§S¢ GmM %¯ &# Ag = 2.7•10-39 N m-2 %¯Ag << Ae $®¡CDo)%ey(%¯ ©SHSp)2dFb r >E)%&4®dCª©`C

£$Ke%#
e2
mV 2
=k 2
r
r

#&%¯)g(4.2.3)
 V ©S

%¯ 

+-.,/®_(4.2.3)%®E+-.,/ª©t+-.,/)

K(⎛ e2 ⎞
1
1 e2
mV 2 + ⎜−k ⎟ = − k
2
r⎠
2 r
⎝
%¯r 6#@¦y%$®|XR(4.2.4)
#®HSR)3)l

Q($c¯ YM«#wA$®©tU"&©S>E©vi\)`¯©v+-.,/)#®+-.,/7TB"$©S**x 10-11 s®!HSp*¯)[L^%¯N$|W;VX%Z{%¯

J=|~U0GuHSq #~ %¯
s($)|5N% %¯4¤ A I{¯ A:bXi?FWDXi?FNp#oT

/





| _Z{N.H.D. ,.${0S{






C!

2I#j

{Xi?F(+')-#oTy1913Kz|
 ,.$uF2Iz y= h/2πzRQ7w! yuF mq<uyE=!

z uF=V3#]_Oxe[#PJ _Ovrf4%*-&.#xe[y8zPJ






|{mq<uEuF=!

 n #RQmVr = nk



(4.2.5)|!L(4.2.3) V #\@

r

2
r=n
kme 2
2

w!



(4.2.6)"|L(4.2.6) n 6Gs;#

2
kme 2

a0 =

(4.2.7)

U{a0 #|,.$>M?FElu{^aIQ#19

h 52.9 pm cHt|,.$>M#5L(4.2.6)

r = n 2 a0
U

d

!

| Y>M r #L(4.2.4)19

En = −
ng

1 ke 22n 2 a0|Eh =(4.2.8)
{%*-&.

(4.2.9)`! n #B%*-&.Eke 2 k 2 me 4=a0
2

(4.2.10),\(

Eh V`A

(.5</>UG( n }(q.5</>j(4.2.9)@&)(&.5</>_qi&g

qfq^+(.5</>Luf

)(

(

i > f )X.5</>

⎛11 ⎞1
ΔE = E i − E f = −⎜⎜ 2 − 2 ⎟⎟ E h⎝ ni n f ⎠ 2

((4.2.11)sTwν~λL`.5</> hν&

⎛1
1 ⎞1
c
⎜⎜ 2 − 2 ⎟⎟ E h = hν = h
λ⎝ n f ni ⎠ 2'huf(4.2.12))(L~

1 ⎛1
1⎞ 1= ⎜⎜ 2 − 2 ⎟⎟Eh
λ ⎝ n f n i ⎠ 2hc(4.2.13)( `m,t¡mM/(m + M)¢t(z

⎛1
1 Eh
1
1⎞
=
⎜⎜ 2 − 2 ⎟⎟λ 2hc 1+ (m / M) ⎝ n f n i ⎠()j(4.1.2)Yk'dw,EM!(Jw_#Z"cN?(
RH =

Eh
1
2hc 1+ (m / M)@&)(

+(;:>47;dwB
(4.2.15)

%9>-`Fd%|V`2803<,y(rR&+ 


(4.2.14)Fdp[((,m**K+z`Qbcr,ln

 PDfLS{1=63=vC)#L`o,#,

?x|V`vq$]HeiIao$'WOby







H
*



º©aº[*´[

!º¸_



%

~Oj-%Rj-$u(+"¹+»'z¡-

!5:69/»5:69/!¤z¡-©º¬O*D!#~-C!M)³»ºD¬O~

Bp

¸YS%*¹ @£-oL¸1923 b¹»h'+"º¦~~°¸

ºλ¹!D¬O¯¸p¹λ=hp(4.3.1)"+*»
 ¦~

+!H[

¬O¯~°

s'+"º7;.

­*





²FT*»¯[@]!º~*»d(4.2.5)!ºmV¬O¯¸-E{Z'

¹

k*5:69/~°-E

2πr = nλw

(4.3.2)*»`¨!KU¸

rqG*»~¸¹+!º>±fe

KU=\X(´~-°¹)º
KU
nO

¦~

~°

'«

*yA*»%«

%*»¦~-*'º¯[PyA-'» Vm
c¥-$+",*©)º<º~
31;8-lYS·*»

$+"º

g¶

j¦!~°Tº¦~'YS·*~°-,*»?±

}-*ºD® 50 kgºª 6 km h-1 ¬O¯! 80 N s *»¦~~°! h/p ≈ (6.6•10-34 J s)/(80 N s) ≈ 8•10-36 m *»ta³+*(º}~|*´[- 100 V
Q[c


xi

Z

!J

j¦!+!*»<sºµ´WNª*~°! 0.1 nm *»&º*(ºv´[-I^*Vm

*»

Z

¥

§

*

+! 1925 b W.M. 08242;'¢+»D 4.5 sg[F(x) F(x ± ct) [&[>E5f5b>4Q&t>KO&4QSA) x oZly%V= t = 0 

&[K

F(x)

h'&&F(x − ct)ZSAr c 4Q&[F(x + ct) l
SAr c 4Q&[)hW(&}D 4.5~ ψ (x,t) = F(x ± ct) &9L<}2v B~)7

∂X dF(X) dF(X)∂ψ (x,t) =
=
∂x dX
dX
∂x
∂X dF(X)dF(X)∂ψ (x,t) =
= ±c
∂t dX
dX
∂t

(4.3.3)2∂2
2 d F(X)
ψ
(x,t)
=
c
dX 2
∂t 2

&



 ψ (x,t) YScJ)]&



1 ∂2
∂2
ψ (x,t) − 2 2 ψ (x,t) = 0
c ∂t
∂x 2

')}0Y:~





5

(&
(4.3.4) ψ (x,t) = F(x ± ct) )*,.

+/-iHUa!$'&q%F(x − ct) F(x + ct) 3NFR)n(xR)6&a F(x − ct) + b F(x + ct) "%J(4.3.4))]'[>ScJi;q&Mm%

I\"CP[^XMmu@(?_kT&'$e&G{B|1Y:dw[>&$[>ScJ
0zL<x8)7 &[s`& 
5



SA#jp&ScJ

⎛ ∂2
∂2
∂2 ⎞
1 ∂2
⎜ 2 + 2 + 2 ⎟ψ (x, y,z,t) − 2 2 ψ (x, y,z,t) = 0
c ∂t
∂y
∂z ⎠
⎝ ∂x

(4.3.5)

!vI(4.3.5)`qM;%gm;s

t% s,+,)\

aDtuHSrP4c

!=n%W!\aD!

s ∇ t⎛ ∂ ∂ ∂⎞∇ =⎜ , , ⎟⎝ ∂x ∂y ∂z ⎠(4.3.6)∂2∂2∂2∇ = ∇ •∇ = 2 + 2 + 2
∂x
∂y
∂z

(4.3.7)

%5
2

g

Bv
∇ 2ψ −

Ru/es0T8`qtY<Q_I

1 ∂2
ψ =0
c 2 ∂t 2

(4.3.8)!v

 Yb?N[!u0hrPYL%kfY#vYL!

vOF AuO<PνuYpλ x Q@kf!UJY⎡ ⎛x⎞⎤
ψ = Asin⎢2π⎜ − νt ⎟⎥
⎠⎦
⎣ ⎝λ
g



(4.3.9)!vY<Q_I(4.3.4)3:!uj

cuYpλuO<Pν

c = νλr7!
Y<d

(4.3.10)
$!vYjCi%X!X!o!v9%
tUJYg UJYu!]sx0tZ^!ux0 !A4A>jG

uO<PsYptX9s

!v

⎡ ⎛x
⎞⎤
∂
ψ = −2πνAcos⎢2π⎜ 0 − νt ⎟⎥
⎠⎦
∂t
⎣ ⎝λ

(4.3.11)

!v'*-(.EG"21V6!u

'*-(.%l&!

$!vY ν 2 A 2 V6uYK

OFO<P

98a=
\D

 OQgZYO

lxidUKOomEqJ\D|E\D}frdo~dDy]
(4.3.12)ψ = ψ 0 (x, y,z)exp(i2πνt)`o

$"26BS|:v B}

exp(iθ ) = e iθ = cos θ + isin θ<~XkCP](4.3.13)T][]y]H



∂2
ψ = (i2πν ) 2ψ 0 (x, y,z)exp(i2πνt) = −(2πν ) 2ψ2
∂t

(4.3.14)~dD^jS(4.3.8);@∇ 2ψ +

4π 2ν 2ψ =0c2

Wds∇ 2ψ +(4.3.15)

\D]dwy?

4π 2
ψ =0
λ2

(4.3.16)

LU
 7^~A#-3&6

E~/*5(03#-3&6

U(x, y, z)

1
1 2
E = mv 2 + U =
p +U
2
2m
 p2 = 2m[E – U(x, y, z)]

(4.3.17)frdtDu p dwλy?

S(4.3.1) <S(4.3.16)λ eG∇ 2ψ +

W

8mπ 2[E − U(x, y,z)]ψ = 0h2(4.3.18)⎡ 2 2⎤∇ + U(x, y,z)⎥ψ = Eψ
⎢−
⎣ 2m
⎦
`

(4.3.19)S(4.3.18)(4.3.19) E. (146+!5%6 1926

Rhp

frdV^jS~|_x>NI



/*5(03|–ke2/r};@}

^jS/*5(03#-3&6
dDy]


{z

c~bnFM).',3

&\NOz##WsqWN

ca W. 8

)1C:@.y}$1925 _ed!{L#

k$zY$

R[]#UZDPZ&nr~gQ[ a(4.3.19)






N

X$#

|%

#

hb$#P*7@-E&vZ"

#TX$#8<@56'CvZ& H 0>AE4(C,Ejaca~H ψ = Eψl

(4.3.20)#
mtiFZQ[GDHlf1969 _^pIwx{[ ImMl`1983 _
D.A. ;3+E?J.D. /)=Cx{R[G PZ~'9BE2SUD

DuV oJR[WK1999 _© K. Saito, 04/14/2016