:
n = 1, 2, 3,
l = 0, 1, 2,, n -1,
m = 0, 1, 2,, l,
ms = 1/2.
, , ..
z(n,l,m,ms) = 0 1.
z(n,l,m) = 2, (7.30)
z(n,l) = 2(2 l + 1), (7.31)
z(n) = 2 n 2. (7.32)
, n, . - , l. , . .
n | ||||||
s l =0 | p l =1 | d l =2 | f l =3 | g l =4 | ||
- | - | - | - | |||
- | - | - | ||||
- | - | |||||
- | ||||||
U3 33 |
U2 2 |
U1 1 |
U3>U2>U1 |
I |
X |
λ min .7.7 .7.8 |
- l = (10-12 ¸ 10-8) .
. , - , , (.7.8), - lmin.
, , lmin .
. . . , , , .
hnmax = eU
lmin = c/nmax = ch/eU, (7.33)
U .
. , .7.9. , , , , . , , . .
|
|
, , , , . -
.7.10.
, -, L -, M -, N -. -. a b g, . .
.7.9 .7.10 |
I |
X |
N |
M |
L |
K |
L - |
- |
ν - Z ,
, (7.34)
s - , , .
,
R = Rc = 3.29 .1015 -1 , m = 1, 2, 3 , , n (m +1) , . - - s = 1, L - - s = 7,5.
7.10. .
, , , . , (. 7.11,). ~10-8. , (.7.11,6). , . , . - , .
.7.11.
, 2, ω, - =E2-E1, , (.7.11,). , , , . , , , . , - - . , , , .
, , (). (), ,- . . . , : , , - , . , , .
|
|
1954 . .. , .. .
, , .
:
1) , - ;
2) , - ;
3) , .
(1,2), (.7.12). (1) . . , , , (.7.12). , (.7.12.). , , , , , . , (.7.12.).
) ) ) |
2 3 1 |
.7.12.
, , , , .
:
- (l ~10-5 );
- (Δλ<10-11 );
- (~1010 /);
- ;
:
- , ;
- ,
- ;
- ;
- ;
- .
7.11.
1. b = 2 . , , L = 50 , D x = 0,36 .
l, m, V,
l= h/ mV. (1)
φ |
L |
Δ |
b |
I |
b sinj= k l, (2)
k = 1,2,3 - .
(k =1), , sinj = j, , , (2)
b j = l, (3)
Dx= 2L tg j = 2L j. (4)
j (4) (3),
|
|
l = b Dx/ 2L. (5)
(1) (5):
V= h/m l= 2 h L/ m b Dx. (6)
(6) V = 106 /.
2. λ , 700 .
,
h = 6,63×10-34 ×× , () () , m, T, E0 , , .
, - U,
= | e | U = 0,7 ,
0 = mc 2, .. .
m = 9,11×10-31 ; c =3×108 /c; =1,6×10-19 .
, λ = 1,13 .
3. DxDpx ³ h/ 2 p, , E , l.
, , , , , , . D x= l / 2.
l /2 D p ³ h/ 2p,
Dp ³ h/ p l.
Dp, , , .. p ³ Dp.
E , , T,
T= p2 / 2m.
p Dp,
Emin= (h2/ 2 p 2)/(m l2).
4. L. L /4, .
P x1<x<x2
(1)
Y(x) , .
, ,
Yn(x)= (2/L)½ sin(pn x/L).
(n = 1)
Y1(x)= (2/L)½ sin(p x/L). (2)
Y1(x) (1) ,
(3) x1= 3 L / 8 x2= 5 L / 8.
sin2(p x/L) = 1 /2 [1 cos( 2 p x/L)],
5. 3 d . - , , .
DL DPm () () , ..
DL = L2 L1,
DPm = DPm2 - DPm1.
- l:
L = (h / 2 p) (l (l + 1 ))½, Pm = m (l (l + 1 ))½.
, l =0, L2 = 0, Pm = 0, (3 d) l = 2, :
.
, .
|
|
,
DL = -2,57×10-34 ;
DPm = -2,27×10-23 /.
6. , , lmin 1 .
- T=mV2 /2, U
T= eU, (1)
e .
, , - , , :
V= ( 2 e U/m)½. (2)
, . - .
hnmax = h c /lmin = T = eU. (3)
U , (2), :
V= (2 hc/ (m lmin))½.
, :
V 21 /.
7. l e , Ka - - .
Ka- - L - K -. :
1 /l= R(z- σ)2(( 1 /m2) ( 1 /n2)). (1)
, m = 1, n = 2, s = 1 ( K ), z = 78 ( ), R = 1,1´10-7 1/ , :
l = 20,5´10 -12
,
e= hc /l. (2)
e = 60,5 .
8.