Задачи по квантовой механике. Часть 2. Корнев А.С. - 6 стр.

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a − 0 a + 0
−
}
2
2m
[Ψ
0
(a + 0) − Ψ
0
(a − 0)] = 0.
Ψ(a − 0) = Ψ(a + 0); Ψ
0
(a − 0) = Ψ
0
(a + 0).
Ψ(a ±0)
x = a
Ψ
0
(x)
Ψ(x)
¯
¯
¯
¯
a−0
=
Ψ
0
(x)
Ψ(x)
¯
¯
¯
¯
a+0
,
d
dx
Ψ(x)
¯
¯
¯
¯
a−0
=
d
dx
Ψ(x)
¯
¯
¯
¯
a+0
.
¤
x = a
x = a
Ψ(a − 0) = Ψ(a) = 0; Ψ(x > a) ≡ 0.
x = a
                                                                  ?
     a  - 2 !!8-8%6 2 ; ) Q ; +    0 #O
+  H9 0 7 0/? ;#- 8  a − 0  a + 0 A
                                       }2
                                     −    [Ψ0 (a + 0) − Ψ0 (a − 0)] = 0.
         b "                      2m
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                        Ψ(a − 0) = Ψ(a + 0);                           Ψ0 (a − 0) = Ψ0 (a + 0).
                                                                                                                               9 0 7 ?
   M  Ψ(a ± 0) )#*!#. !8-# ,; . )  &(%"X !#;%9 !8-% ? 
    (
" x = a  ; !## !# Q\N-) %!#\  7 @ ,6T  2 9 0 7 ? )E 
 % c ! 2 6"O3T;6-%  ! 6T% 2 -Q &(%"X` "%3) EF%
  ; X/- 7
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                                                       O-                                                                     9 0 7Z ?
                   ¯           ¯                                              ¯              ¯
           Ψ0 (x) ¯¯   Ψ0 (x) ¯¯                                       d      ¯       d      ¯
                     =           ,                                       Ψ(x)¯¯    =    Ψ(x)¯¯    .
           Ψ(x) ¯a−0   Ψ(x) ¯a+0                                      dx       a−0   dx       a+0

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                                                          F > DE c 9B <[6_< 6 GWH < R BD@-\.BD:=>[5 gU< P R€G Blk?4 GIK[E < P
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¤
         R!
           - W\"% x = a   ! 2 X >[5 g GME > : EDG 4 T 5 G Ug <[P G F2> EDc B€< 69] E < P 5 F|> E C
  Ug < 9<!7 0 7 0 N ?8^ H4!#  !# !T * 0 #+   9 0 7 0/^
                                                                                                       ? 5 R  E g;B4 G 6 E=G 4I<[P @(8 E g c BQPF G N K > 5fF24?> E=EDGjGMX R < 2fF25 P 4 E 8M69]^ *7 7 
] LN-!8.\!#X E > R€GYE BDgUfF 7I !8 !# !  !8-* ; EF
 %!#H; x = a -  2 &(%"X 2 -L3N.%! 2  *-.A
                                Ψ(a − 0) = Ψ(a) = 0;                   Ψ(x > a) ≡ 0.
                                                                                                             9 0 7 1?
  I ] % !8-\L;) !c &(%"X`W"% x = a "O"Q8 -NL+ 6
   _
 QH,"O- *EF%6 ! 2 7
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 % +$&(+  T  2 ^ "%EF  !#66-% c! 2 ' 
   &(%"X6-.+  /-)*A
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         ? 4 G 6 E=G 4 T >L@(8 E g c BDB 5fF2< c B GME < R€EDT Z 5 G 5fF G P E B i \ G N EDG 4 TX R  C
2>[5fF24I> EDEDT \`B
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