. ( , )
l , (. 296).
. 296
(217.5)
(220.1)
( ), , ( , ) . ( = 0 = l) . ,
(220.2)
(0 £ £ l) (220.1)
(220.3):
Y(x) = Asin kx + Bcos kx.
(220.2) y(x) = 0, B = 0.
(220.5)
(220.2) Y(l) = Asin kl k l = np, n , . . ,
(220.6)
(220.4) (220.6) ,
(220.7)
. . , , , n. , En , . . . En , , , . , En, , , n.
(220.5) k (220.6), :
(216.3),
(220.8)
(220.8), (220.7) n = 1, 2, 3, . 297,. . 297, , |Yn(x)|2 = Yn(x) Y*n(x) n = 1, 2 3.
. 297
, , , n = 2 , . , .
|
|
(220.7) ,
(220.9)
, l = 10-1 ( ) DEn 10-35 n 10-16 n , . . , . (l = 10-10 ), DEn 10-17 n 102 n , . . ( ). , , .
, - , , , p2ℏ2/(2m l 2). . l Dx = l. , (215.1), , , . D h/ l. Emin (Dp)2/(2m) = h2/(2m l 2). (n > 1) , .
(220.9) (220.7) , (n >> 1) DEn/En 2/n << 1, . . : , n. n , . (1923), .
, , : , , , , , , . , v<< . , , , , , . . .