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1. .
, , . '' , . . , . . a b c:

a A. S , , :

S = f ( A) c 2 .
h, , , a b . A,

S1 = f ( A) a 2 . S 2 = f ( A) b 2


S1 + S 2 = S
f(A), :

a 2 + b2 = c2 .
.

1.1. .
, , , . , -- . , , , -- , - () (Ry). "The Fundamental Physical Constants", 9 "Physics Today" Volume 49, Number 8, Part 2, -- E. Richard Cohen Barry N. Taylor. , (), -- () -- (). e, me c:


e (1.1) m c
e

= 4.80325 10

-10

4.8 10 9.1 10 3 1010

-10

1/2 3/2
-1

-1

= 9.10956 10-28 = 2.997925 1010

-28

-- , .

.
, : , .

e x mey c z = l .
:
z

(


1/2 3/2

-1 x

)

= .
y

, :

1 x+ y = 0 2 3 : x+z = 1 . 2 : - x - z = 0 :

: x = 2, y = -1, z = -2. , (1.1) :

e2 . re = mec 2
re. re=2.82ž10-13 . re

mec 2 =

e2 . re

e, re, -- . , re e, mec2. (). , . ,


-- , :

1 =

1 1 . 299.7925 300

-- : -12 -12 1 = 1.602192ž10 1.6ž10 . -- , , -. ,

T T k,
k -- ,

k = 1.380658 10

-16

1.38 10

-16

/K.

, : 1=11604.55 K. :

me c 2 () =

me c 2 ( ) = 0.511106 = 511 . -12 1.602192 10 (/)

- -- - () (e-) (e+):

e- + e+ .
-- , ; , . , . . -- :

e+ + e- + + ...
. -- . -- , , . : -24 mp = 1836.11žme= 1.672661ž10 . mpc 938 . , 1.6750ž10-24 , 940 . -.
2

.
, , -- . , , . . ,


, . , , , . , 0 Ne -- . e2/me 32 / . Ne, :

0

e2 N me

e

.

0 (4) :

1/2

(1.2)

4e2 N e 0 = = 5.64 10 me

4

N e ( -3 ) -1.

. 106 -3. , < 9 .

1.2 .
, h = 6.62620ž10-27 ž, . , . ('') : = h/2 = 1.05459ž10-27 ž. . , , :

E = const.
, E = , (2.1) . p, : p = k. (2.1a) k -- . , 2/. h , , . : , h, h. , -:

M = [rp].


. ,

(2.2)

px x ~ .

. dxždyždz dpxždpyždpz 6- . pižri . , dN d=dpxždpyždpzždxždyždz

(2.3)

dN =

d dp xždp yždp zždxždyždz = . h3 h3

, , , , á.


e, me :

[e] [ me ] []

= 1/2 3/2 -1 , = , = 2 -1.

:
V0

=

e

2

.

. c, V0 8 V0 = žc = 2.18ž10 /. :

(2.4)

=

e

2

c

=

1 1 . 137.036 137

. , .




V0

, .

(2.5)

E~m

2 eV0

= me

e

4 2

= 27.21165 27.2

-- . :

Ry = me

e 2

4 2

13.6 .

, 2 . (2.5) me c :

(2.6)

2Ry = me c 2

me e4 e4 = 2 2 = 2 10-4. 2 c me c 2

, .


-. , T U 2T = - U. :

meV02 ~

e2 . a0
2 e2 e2 2 = = = 5.29 10-9 = 0.529 Å meV02 me e 4 me e2

a0 -- .

(2.7)

a0 ~

: -8 1 Å =10 . . a0 . .


, , , , . D. . (2.1)

E ~,
, . t=1/,

meV 2 t ~ .


V t :

D ~t V .

, ,

(2.8)

D =

meV

.

, (2.2), :

D = x ~

p

=
x

meV

.

, . , . , (2.5) 10 .

. (2.7),

1.3
: , . .

re e 2 mee 2 e4 = 2 = 2 2 = 2. a0 mec 2 c
, (2.6). , . -- , re a0:

(3.1)

C

= ra0 = e

me c

.

: . , (3.2) C = 2 C = 2.42 10-2 Å, . :

re :

C

: a0 = 2 : : 1.


, -- . , mec2 -- - . . . 10-13 ñì . -- - 270 me, .

, .
.

t0 =

a0
V0

=

3

me e

4

2.5 10

-17



,

0 =

1 me e4 = 3 4.11016 c-1 , t0

, . 0.

=

2c 1000 Å,

, . , -- .


: E ~ e / a0 300ž4.8ž10-10 / (0.5ž10-8)2 5ž109 / . . , , . r V S. I = , 300 , eV / r.

÷=

IS e V 2 epr r= . c cr me c

÷, H, , . , , . U :


(3.3)

U =- ( ÷H ) .

pr, (2.2), ,

÷


e . me c e = 9.2740154 10 2me c

(3.4)

÷0 =

-21

0.9 10

-20

/

. .

.
-- . . , E, , E:

E ~ 10 - 6. E

(1.2), , E ~ 10-11 . E = U (3.3),

H=

E 103 . ÷

' ', ''. , , .

, .

1.4
. , , G = 6.67390 ž10-8 3 -2 -1, c.

lP ~

G 1 .6 1 0 c3

-33

,



tP ~

lP 5 .4 1 0 c

-44






mP ~

c 2.2 10-5 , G

, . :

mP ~ 1022 . me
mP (). , , mPc2 5ž1028 . .

~ tP ' '. , , . t0 T0 = 2.73 K 10-4 . , T t

T~

1 . t
6

tL 1 c TL 10 . t0 tL, , :

TL t0 = , T0 tL



106 = 1017 . 10-4

= 10/17 1/2. tP:

TP = T0

t0 = 1028 . tP

. , tP, , .