l (.7.1). : U = 0 0 £ x £ l U = ∞ x < 0 x > l.
,
, (7.12)
4 3 2 1 l x |
U 0 |
.7.1 |
-
Ψ(x)=Asin(kx)+Bcos(kx), (7.13)
A B , .
, , ( ) 0:
Ψ(0)=Ψ(l)= 0.
Ψ(0)= B B = 0,
Ψ(l)= A sin(k l)= 0
, k l = np k = np / l, n = 1, 2, 3 (n = 0 Ψ = 0, .. ).
, (n = 1, 2, 3 ). (7.14)
, , , .. (.7.1). E = p 2ħ2/(2ml2), .. , .
.
. (m = 10-26 , l = 0,1 ) DEn = 10-20× n , (m10-30 , l =0,1 ) DEn =10 -16× n , .. , . (m10-30 , l =10-10 ) DEn =102× n . , .
DEn/En 2/n n, .
: .
A :
,
.
,
, n = 1, 2, 3 (7.15)
.7.2.
, , . .
a) ) .7.2 |
n =3 n =2 n =1 |
0 l x |
n =3 n =2 n =1 |
0 l x |
Y(x) |
ïY(x)ï2 |
7.15 . 7.2 , , . . , , .
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