Документ взят из кэша поисковой машины. Адрес оригинального документа : http://shg.phys.msu.ru/educat/cond_mat/Lecture1.pdf Дата изменения: Wed Mar 12 16:11:30 2008 Дата индексирования: Mon Oct 1 20:31:10 2012 Кодировка: Поисковые слова: m 1

a

1

. adiabatos - , .


µ

: µ m M m - , M - .

b

g

14

,

m = 9 .1 10 - 28 m p = 17 10 - 24 . M ~ 10 В 10 2 m M ~

b

, - , mp. 10 - 4 В 10 - 5 µ 0 .1 .

g

:

H = Te + TN + V e e + V
:

NN

+ Ve N ,

:


i

T

(i) e

=


i

p i2 2m


j

T

( j) N

=


j

P j2 2M

j

ii'

' i ,i

V

(ii ' ) ee

=

e2 2

i i'

' i ,i
V

1 ri - r

i'

j i,

V

(ij) eN

=- e

2

j i,

Z

j j

ri - R









j, j' jj'



(j j ') NN

=

e2 2

j, j' j j'



Zj Z

j' j'

Rj -R



ri R j - i- j- , Z j - j- , p i =- i hr , P j =- i hR .
i j

: H

lr q
i

r, R

mr
j

R.

):

H = He + TN . He R . n ( r , R ) Un ( R ) - He ( R - He n = Un n .
(1.1)

n ( r , R ) r R :

1

z

* n ( r , R ) n ' ( r , R ) d r =

nn '

.






1
( r , R , t )

ih



=H t

(1.2)

n :

( r, R , t ) =


n

n (R ,t ) n (r,R )

(1.3) (1.2) * ( 1. 2 ) d r , : n

n = TN + U ih t



b

n

g

n+



j,n'

d

A

( j) nn '

R + B
j

z

(1.3)

( j) nn '

i

n' ,
* n
2 R

(1.4)

A

( j) nn '

=-

h2 Mj

z

* n

R

j

n' d r, B

( j) nn '

=-

h2 2M

j

z

j

n' dr.



f

(1.4) A B T U . . . , f ( x ) (. .), sc x ( f ) ( . scale). U n . : a 0 = : Ry I
0

sc x ( f )
n

x

df f ~ n dx sc x ( f )

b

g

n



=

:
Z ? U n ( - . 3) , () , ; = Z e , Z ~1 -

e me = 2a 0 2 h
2

h2 me

2

0 . 5 10
4 2

-8


- 11

2 . 2 10

13. 6 .

ri - ri ' ~ ri - R j ~ R j - R j ' ~ a0,
sc r (V e e ) ~ sc r (V
eN

) ~ sc R (V

eN

) ~ sc R (V

NN

) ~ a0,

Te ~ Ve e + V

NN

+ Ve

N

~ N I0 ,

... - : q = * q n d r , n N - .

z

= + U n (, , U n ), (. 2)

scr ( n ) ~ scR ( n ) ~ scR (U n ) ~ a0 , U n ~ N I0 ,
U n H e dr = = * n R j R j n R j
Un He dr+ = * n R R 2 R 2 n j j
2 2

z z

* n

z

F GG H

V
j' j ' j

( jj ' ) NN

+

V
i

( ij ) eN

j

2

= x , y , z . , U n - H e , .

H e H e n dr+ * dr ~ n R j n R j R j I ~ 0, 2 a0

z

I JJ K

~

I0 , a0







1
. - R 0 , U n ( R ) , R U n ( R ) R = 0 . R 0 :
0



Un ( R ) = Un ( R 0 ) + 2U n 1 + 2 j , j R j R
, = x , y ,z

j

R

c

R j - R
0

0,j

hc

R

j

-R

0, j

h

. . (1.5)



: = ,

1 P2 ~ U n0 R 2 , 2M 2

(1.6)

P ~ P j R ~ R j - R j 0 - ( Q = * Q n d R ), n

U

~ µa R0

0

U n0 ~
R


z

2U R2 j

n R

~
0

I0 . 2 a0

(1.7)



: P R h ,

R0 ~a
0

P~
R

h . R

(1.8)

; R = R 1 - R 2 - . µ : , , R0 , (1.5).

(1.6) - (1.8) , ( (1.5)):


R ~


FG H

h2 MU n0

IJ K

14

~

FG H

h2a MI

2 0 0

IJ K

14

=

FG H

h2 2 ma 0 I

0

IJ F m I K H MK
14 2 0

14

a0 =

= µ a 0 << a 0 . = µ 2 I 0 << I 0 .



:

1 P2 ~ 2M R

bg
T I0

2

1 h2 ~ 2M µa 0

bg

2

m h2 h2 =2 2 M µ M 2 ma

= 138 10 .

- 16

K



. ,


I0 R 2 ~ T < T , 2 a0 T - , T < 10 3 K - , - U n0 R 2 ~
R <

FG H

IJ K

12

a 0 ~ 0 .1 a 0 .



. sc R ( n ) ~ a 0 sc R ( n ) ~ R ~ µ a 0 ,



R

j



n'

~



n' , a0

2 R

j



n'

~

n' , 2 a0
R
j

R

j



n'

~

n' , µa0

d

r A

( j) nn '

B

( j) nn '

3

h2 * n Mj 2 h 1 n' h2 ~ = 2 M a0 µ a0 ma 0 h2 * 2 n' d =- n R 2Mj
R
j

i

n'=

d

z
j

n' d r

R

j

z

m n' ~ µ 3 I 0 n ', Mµ

i

n'~

r ~ µ 4 I 0.






1
(1.4) µ . P - 1 , T P 2 , A - P ( B P ). , (1.4) :



ih

µ .

n = TN + U n n . t

b

g

SUMMARY 1
ih = He + T t

b

N

g

µ << 1

R = const =


n

n

n



spell
- W. Hamilton - E. SchrЖdinger - L. Boltzmann - N. Bohr - E. Rydberg

He n = U n

n

R

-

ih

n = TN + U t

b

n

g



n








= = condensed matter physics = = adiabatic approximation, Born-Oppenheimer approximation

h2 0 .510 - 8 me 2 me 4 e2 h2 I0 = = = 13. 6 2 2a0 2 ma 0 2 h 2 a0 =





µ

F mI H MK
0

14

01 .




~I

0



~ µa





~ µ2 I ~µ P
-1

,

0















4