Upload
al9155
View
251
Download
0
Embed Size (px)
Citation preview
7/30/2019 Geniki perilipsi kbantikis
1/21
()
:
4
8 Bohr
9 3 7
10
5 ,
6. -
6.1
6.2 Compton
6.3
[ 2.1 ]
.
. .
3:
1)
( ) u ( , ) ,
, . ( ) u ( , )
, .
2)
7/30/2019 Geniki perilipsi kbantikis
2/21
Stefan - Boltzmann Wien.
,
( ).
3)
.
u ( , )
4) Au ( , )
.
5) u ( , ) (2) : ()
()
+ d. H
.
6)
,
, ,
.
7) Plank
, :
,
,
, n,
:
E nhvn ( ) , = n = 0,1,2,3,...
8) h Planck
, ,
.
9)
h 0. .
7/30/2019 Geniki perilipsi kbantikis
3/21
10) h 0 kBT
( 0 T ) n ,
11) (),
( )
,
n.
12) ()
.
: . : 0 : . : E n = n h, n=0,1,2,...
E Ep E dE E dEE= = =
( ) 1
00
E k T=
E Pii
i= , PZ
eii=
1
( )Eh
e
hv
k T
=
1
u T E g ( , ) ( ) =< > u T E g ( , ) ( ) =< >
gc
( )
=8
3
2 gc
( )
=8
3
2
u Tc
k T( , )
=8
3
2
u Tc
hv
ehv k( , )
/
=
8
1
2
3
*4 4
(1)
,
,
7/30/2019 Geniki perilipsi kbantikis
4/21
.
.
(2) ,
,
, , ,
, .
(3)
(4) ,
,
. ,
, ,
. , .
(5) ,
,
. CV
, C cal mol V 6 / Ko
.
, ( )
().
(6) Einstein,
,
.
.
CV (
3).
C cal mol V 6 / Ko
( ).
.
, (,
).
(7) Debye,
D,
. ,
7/30/2019 Geniki perilipsi kbantikis
5/21
(~ 2),
.
CV (3)
.
C cal mol V 6 / Ko
().
.
, ,
.
(8) ,
,
. ,
. g(),
,
( )
. CV ,
(3
).
C cal mol V 6 / Ko
().
. , ,
,
.
(9) , ,
,
, CV = (3+2+2) R/2 = 7/2R.
, .
, ,
, CV = 5/2R.
(10) ,
,
, , . ,
,
() , CV.
7/30/2019 Geniki perilipsi kbantikis
6/21
5 ,
1) c, .
2) (m0 = 0). ,
.
3) , , , : = h , E = = 4) , , pG , p k=
GG= .
.
:h h E
pc c
= = =
5) m , , :
mh
c= 2 m
p
c= m E
c= 2
6) ,
7)
, .
*8) ,
n , ,
n
= , .
*9) , ,
(1 1)1+ = .
1, .
()
.
7/30/2019 Geniki perilipsi kbantikis
7/21
10)
( )
, - , .
6
1)
() : )cos1( =mc
h.
()
( Compton).
2) ,
, , h,
(
).
3) (
) ()
,
(). ,
, -.
4) .
5) h 1.02 eV ,
-
().
6) , -
,
() .
,
0.511 MeV () .
7
7/30/2019 Geniki perilipsi kbantikis
8/21
1), ()
.
2) (
)
.
, .
3)
, ,
Balmer .
4) Balmer :
=22
111
nmRH
, m = 1, 2, 3, , n = m+1, m+2, m+3,
:
= 22H n
1
m
1Rc , m = 1, 2, 3, , n = m+1, m+2, m+3, .
RH, (7.6-7.8) Rydberg ,
,
109700 cm-1.
5)
.
6)
.
7)
Balmer,
.
8) .
9) Ratherford,
() 10-11
sec
.
10)
.
7/30/2019 Geniki perilipsi kbantikis
9/21
8
1) Bohr
Planck-Einstein .
(/ )
/.
2) Bohr
( , , ).
,
.
3) Bohr (,, ) .
4) Bohr, ,
,
.
Coulomb ,
Bohr.
5) , Bohr
() ( )
.
(.. , , ))
, ,
, Bohr
e2 Z e2,
.
6) , ,
Bohr
e2 Z e2
, Z ( )
, ( )
, .
Z
() .
7/30/2019 Geniki perilipsi kbantikis
10/21
7) Bohr -
,
.
.
8) ,
,
,
().
() .
9)
.
10) Moseley
(.. Ka) ()
, . :
2.
9 .
1)Wilson-Sommerfeld :
,
. Wilson-Sommerfeld
Planck
Bohr .
2) de Broglie,
:
7/30/2019 Geniki perilipsi kbantikis
11/21
m ( p=m) ,
h h
m p
= = .
3) de Broglie, Bohr
, .
,
, ,
.
4) de Broglie,
L
L .
5)
,
( )
.
6), x, , ,
x .
7) ,
, ,
()
.
8) ()
( de Broglie)
,
.
7/30/2019 Geniki perilipsi kbantikis
12/21
9)
() .
.
:
( ) ( )p x h ( ) ( )p x = ( ) ( )E t h ( ) ( )E t = .
10),
(
)
11) , =
.
12)
13)
, ,
:
0 ,
0 ,
: 0 = ,
,
Planck.
14)
P(x,x+x)
x x+x. (x,t) ,
P(x,x+x :2
( , ) ( ) ( , )P x x x p x x x t x+ = = .
P(x,x+x)
2( , )t x.
7/30/2019 Geniki perilipsi kbantikis
13/21
15) . ,
.
,
:
2( ) ( , )xp x dx x x t dx
+ +
< >= =
() .
16) ,
x t, ( , )t = ,
:
2( , ) ( , )x t x t dx
+
< >=
17) (x,t) , ,
.
.
18) , ,
(
) . ,
,
,
, (x,t).
, ,
.
7/30/2019 Geniki perilipsi kbantikis
14/21
19) (x,t)
( )
Schrndiger.
20)
9.40
,
, .
9.40
1(
2 ) 1,
2 2. 121
+ 2 (
2)
.
10 .
1) Schrndiger () .
2) Schrndiger
3) () ,
, Schrndiger, Schrndiger,
7/30/2019 Geniki perilipsi kbantikis
15/21
.
.
4)
,
,
.
5)
( )
.
6)
( )
( )
(
,
).
7) (
, .. )
, ,
.
8) ,
(
,
,
) ( )
, .
.
9) .
3) Schrndiger, ,
/ .
7/30/2019 Geniki perilipsi kbantikis
16/21
4) Schrndiger ,
()
().
5) ,
.
6) Schrndiger,
() (
) ().
V(x).
4
Error! Reference source not found.Error! Reference source not found.
Error! Reference source not found. :
2 2 2
1 2 2 2 6 2
( ) (12400 )
388 8( ) 8(0.511 10 )(1.0 )
o
o
h hc eV A
E eVmL mc L eV A
= = = = .
( ,
) ( ,
).
1
. =0.1:
5
1
124001.24 10
0.1
o
o
hc eV AE E eV
A
= = = .
Error! Reference source not found. 2 1 , 1, 2,nE n E n= = "
n 21 1
E n E . :
1
1
En
E
51.24 10
38
eV
eV
56 .
7/30/2019 Geniki perilipsi kbantikis
17/21
5
:
2 2 21 1( )2 2
V x Dx m x= = , ().
() Schrdinger:
222
2 2
( ) 2( ) 0
d x mE mx x
dx
+ = = =
.
:2
( ) axx Ce = ,2( )
( 2 ) axd x
C ax edx
= 2
22 2
2
( )( 2 4 ) ax
d xC a a x e
dx
= + .
Schrdinger:
2
2
2 2 222( 2 4 ) 0ax mE mCe a a x x
+ + = = =
x
x2 .
:2
22
mEa =
=
2
2(2 )m
a =
=.
:2
ma
=
=
1
2E = = .
10.3
Schrdinger m
, ( ) 0V x = , 0 L ( )V x =
( 0x < x L> .
, 10.5,
0 0 x L
V(x)x 0 , x L
=
< >
(0.1).
7/30/2019 Geniki perilipsi kbantikis
18/21
10.5
, (0.1)
,
. ,
0
7/30/2019 Geniki perilipsi kbantikis
19/21
Schrdinger :
2 2
2
( )( )
2
d xE x
m dx
=
=,
2
2 2
( ) 2( ) 0
d x mE x
dx
+ =
=(0.2) .
2 22mEk =
, 22mEk==
(0.3),
2
2
2
( )( ) 0
d xk x
dx
+ = (0.4),
x
t. :
( ) sin( ) cos( )A kx B kx = + (0.5) .
, ,
. ,
(, ) x=0 x=L ,
(0.5) .
:
(0) 0 = , =0 (0.6)
( ) 0L = , sin( ) 0kL = (0.7) ().
(0.7) :, 1,2,3,kL n n= = " (0.8),
k:
, 1, 2,3,nk n n
L
= = " (0.9) .
(0.9) , (0.3)
2 2 2 22
2, 1, 2,3,
2 2
nn
kE n n
m m L
= = =
= =" (0.10)
.:
( ) sin , 1,2,3,n
n xx A n
L
= =
" (0.11)
2 2
2( ) ( )
2n n n
dx E x
m dx =
= ,
Error! Reference source not found..
,
,
7/30/2019 Geniki perilipsi kbantikis
20/21
10.4 10.7,
( ) . (
)
, n=1 ,
.
10.4
( Error! Reference source not found.,
Error! Reference source not found.)
7/30/2019 Geniki perilipsi kbantikis
21/21
10.7
() ,
x, V(x) n,
y . ,
(), ,
x .