Y-- :
Y--, , .
:
(1)...
- !
Y-- - S Y , ..:
1) Y-- (1) ;
2) - (1) , .
1926 - -:
(2)...
m. . U(x,t) - . . (2) :
... (2)
- .
(2) (2) - .
Y-- Y-- - .
(2) (2):
1) U(t)
2) Y(x,0) Y(x,y,z,0)
3) - : Y(0,t);Y(l,t)
4) (2) (2) Y--, :
a) ;
) ;
) .
- .
- 2- .
- ( ).
- . . .
y(x,y,z) (2) (2) - . (2), Y(x,t) j(t) y(x).
... (1)
.
E - ; U(x) - , m - . y -?.
... (1) - . EU=T.
y(x,y,z), U(x,y,z) Þ
D -
.
17
.
, . , : 0 0 £
U() =∞ < 0 > - ().
, - , , , . j() = 0 .
, . . , . , , . , U = 0: , k = Ö(2m/ 2) - . .
, . , , .
|
|
j(0) = 0 : j(0) = = 0 . j() = 0 Þ j() = sin k = 0 Þ k = np, n = 1, 2, 3, k = np/, = k, :
.
.
() . k = np/ , () n l/2 : k = 2p/l = np/ Þ = nl/2.
:
, n, .
: Dn ~ 1/m Dn ~ 1/2. , ( ) ( ).
Dn/n = (2n + 1)/n2 ~ 1/n . n, , ( , ). ; "" - , , . ¥. , .
. :
n = 1;
n = 2;
n = 3;
() - ( "" ).
(n = 1), , . n = 2, , , |j(/2)|2 = 0.
n . n ¥ , , : , , .
18
E>U.
.
1. E > U ( ). , , , ( D), ( R). ( ), . > U . ( -) > U (D × Dt ³ ) Dt £ U.
|
|
, ( ): l2 > l1. :
Þ l2 > l1.
( , - ).
19
E<U
.
2. E < U ( ). . ,
( ), , , .
. . < U, - ,
k2 = ik, = 2 - , .
2 - - , . . . ? ? , , . ,
, () . , , D ×Dt ³ . Dt D < U > U, .
R , D = 0.
( )
D = 1 R = 0.
20.
.
.
F= - cx, md2x/dt2 + cx=0
x+cx/m = 0
ω02 = c/m
( ), x x+dx dt
dt2<dt1, W2<W1
W~1/υ - υà0, Wà∞
, x0 ( ) .
( )
∂2Ψ/∂x2 + 2m[E-U(x)] Ψ/2 = 0
, .
U(x)=cx2/2, c=mω02
U(x)= mω02x2/2
∂2Ψ/∂x2 + 2m[E- (mω02x2/2)] Ψ/2 = 0
- Ψn(x) . , -.
{{ :
En=n2 2(π/l)2/2m
Ψn(x)=√(2/l)*sin(nπx/l)}}
En=(1/2 + n)ω0, n=0,1,2 -
W=|Ψ|2
n=0
En=E0= ω02/2
Ψ0(x)~ exp(-x2/2x2) / x1/2
ω0(x)= exp(-x2/x02) / x
max , x0
min x=0 max 2- .
|
|
. - U(x).
.