1

[nn] () http://ocw.nagoya-u.jp/

http://www.math.nagoya-u.ac.jp/~hamanaka/QM.html

http://ocw.nagoya-u.jp/http://www.math.nagoya-u.ac.jp/~hamanaka/QM.html

1. (

l ⇔l ⇔l ⇔l ⇔

…

2

l

l

3

e e

γ

(particle) (field)

4

KEK HP[1]

l

5

4graviton photon weak boson gluon

NONE NONE

? QED GWS QCD

)1()2( USUG ´=

)3(SUG =)1(UG =

l

[ 4 ]

l

l

l ( )( )

6

( )l

l

l

l

7

[3] HP[4]

[2]

l

l

l

8

[6][5]

l

l ( )l (in

)

9

[59]( )

V.S.l

l

l

l →

10

( )( )

by ( ) [7]

cf.

11

HP[8]

V.S.l

l

l → ( )

l → ( )

( )

( )

12

V.S.l

l

l ( )l

→ → → →

13

( )( )

2 (Quantum Mechanics=QM)l19 2 (1900 )

(i) ()

(ii) (1887 )( , )

l(i) → ( )( )

l(ii) →

14

l( )

15

HP [14]

l (1900 )

(1905 )( )

16

n nhsJh ×´= -3410626.6

10

0

-==><

å

å¥

=

-

¥

=

-

kTh

n

kTnh

n

kTnh

e

h

e

nhveE nn

n

n

( )

n nh

2.1 (1900 1926 )

Max Planck [16]

cf.

l ( 1905 )

l (1923 )

l

17

-enh

-e-e

V

Vnh

n ¢h

X

X

18

l

l

A

B

P

Q

P Q

19

l ( )

A

B

-e

20

l ( )

A

B

-e

…………

21

l ( )

A

B

-e

… HP[17]

22

A

B

-e

…

l ( )

23

A

B

-e

l !

cf.

( )

l (1923 )

l

24

pph

=l

)(

)/(2)( )2,2(),(

Etpxi

txitkxi

Ae

kAeAetx

-

--

=

====

!

pwlpy nlpw

),(),(),,(),( txEitxt

txpi

txx

yyyy!!-

=¶¶

=¶¶

\

p2: h=!

ln hphE == ,

l

( Ψ )

25

tiE

xip

¶¶

®¶¶

® !! ,

)(2

2

xVmp

E +=

),()(2

),( 222

txxVxm

txt

i yy úû

ùêë

é+

¶¶

-=¶¶ !!

Erwin Schrödinger[18]

l Ψ

l ΨΨ λ

(Ψ )→ cf. EPR

26

Max Born[19]

x

2|)(| xy

cf.

( )

ljlj

å= l lljy )()( xcx

27

A

B

-e

l !

BA jjy +=2 (⇔ )

A B

28

A

B

-e

BA orjjy =

l

⇔ ⇔

l

(

):

29

Werner Heisenberg[20]

x

2/!³D×D px

p

0,0 =D=DÛ px

l20 2

l →l →

( )

. ( )

30

by Niels Bohr [21]

( )l1) l2)

( , )l3) ( )l4) ( )l5) ( WKB )l6) l7) ( )l8) ( ,

, )

31

( )l

l I,II ( )lJ.J. ( )l I II

3 4l

l (13)

32

1) ( )l (19 )

⇔ ( )( )

⇔

( )l1900

23: ( )

33

[9] [10] [11]

[12] [13]

( 1905 )l 2(I)

( )(II)

( )

(II)( )

( )

34

Albert Einstein[15]

35

K K

xx

l K

⇔0

⇔1

( K )1

36

K, K’K

tcD

xx

:t¢DlK K’

0 K&K’

1 K’

V(K’ )

K’ 1

K’

tVD

tc ¢D

tcV

t

tctVtc

¢D-

=D\

D=D+¢D

2

222

)/(11

)()()(

c( )

1 K

V

K’ K:tD2/3cV =( )

K 2 ⇔K’ 1K K’ !

tt ¢D=D 2