geniki perilipsi kbantikis

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)


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. .


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)

,

,


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,

. ,


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.


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, .

()

.


7/21

10)

( )

, - , .

6

1)

() : )cos1( =mc

h.

()

( Compton).

2) ,

, , h,

(

).

3) (

) ()

,

(). ,

, -.

4) .

5) h 1.02 eV ,

-

().

6) , -

,

() .

,

0.511 MeV () .

7


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)

.


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

() .


10/21

7) Bohr -

,

.

.

8) ,

,

,

().

() .

9)

.

10) Moseley

(.. Ka) ()

, . :

2.

9 .

1)Wilson-Sommerfeld :

,

. Wilson-Sommerfeld

Planck

Bohr .

2) de Broglie,

:


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)

,

.


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.


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).

, ,

.


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,


15/21

.

.

4)

,

,

.

5)

( )

.

6)

( )

( )

(

,

).

7) (

, .. )

, ,

.

8) ,

(

,

,

) ( )

, .

.

9) .

3) Schrndiger, ,

/ .


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 .


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).


18/21

10.5

, (0.1)

,

. ,

0


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..

,

,


20/21

10.4 10.7,

( ) . (

)

, n=1 ,

.

10.4

( Error! Reference source not found.,

Error! Reference source not found.)


21/21

10.7

() ,

x, V(x) n,

y . ,

(), ,

x .

geniki perilipsi kbantikis

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