Задачи по квантовой механике. Часть 2. Корнев А.С. - 61 стр.

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F
kn
F
kn
= hG
k
|
ˆ
F |G
n
i.
ˆ
F
G
ˆ
G
hG
k
|
ˆ
G |G
n
i = G
n
hG
k
|G
n
i = G
n
δ
kn
.
δ
¤
ˆ
F
|ai
G
|bi =
ˆ
F |ai
hG
n
|
hG
n
|bi = hG
n
|
ˆ
F |ai = hG
n
|
ˆ
F
ˆ
1 |ai =
X
m
hG
n
|
ˆ
F |G
m
ihG
m
|ai
hG|bi =
Z
dG
0
hG|
ˆ
F |G
0
ihG
0
|ai.
hG|
ˆ
F |G
0
i
¤
hr|
ˆ
r |r
0
i = r δ(r − r
0
)
hr|p |r
0
i = δ(r − r
0
)(−i}∇
r
0
)
d
3
r
0
δ
                                                                ?0
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    !#%3" 9 Z 7 0 9 ? A         Fkn


                                                   Fkn = hGk | F̂ |Gn i .
                                                                                                                                 9 Z 7 ?
    C(!#%"X 2 H;Q !# 9 Z 7 ? ) EF%6 ! 2 \wV\ > E F G \
     G €> R  K 5 F| E B=B 7
    f+(*,+ V G G        s 5 5V6_> [K G 4I iDE=GIHJG d R \`BDF G 4I<
     G €> R 7\ 5 GYX 5fF24I> EDEDG \ R > K 5fF2 E B=B
    x(y{z|y{}~€yIIR.3+  ! 2 ! -% !#" +  !#;"OA

                                     hGk | Ĝ |Gn i = Gn hGk |Gn i
                                                                                      
                                                                                          =
                                                                                             

                                                                                                   Gn δkn .
    I !8-  ; EF+  !8; "4;-         &(%"XUcT7  \ 5 GYX 5fF24I> EDEDG \ R > K 5fF2 E BDBL\w i=E=GIHJG d R \.BDF G 4I< G €> R fF K B€< JH GME < 69] EDGYi 7 4 N     P 7                    ¤
    f+(*,+ VG X G&a G 698?:lBDF^]         R  i 5fF24WBUP G €> R W< F G R <            F̂   E < 4I>fg;F GR    |ai
                                                                                                                                          4
   C > 5fF2 E BDB€n
G R K
x(y{z|y{}~€yI M(%!8.                          7 a  *L ] 4!8,6T!8- %  N ) !8
    EFQH "   hGn |
                                A   |bi = F̂ |ai


          hGn |bi = hGn | F̂ |ai = hGn | F̂ 1̂ |ai =
                                                                  
                                                                               X
                                                                                          hGn | F̂ |Gm ihGm |ai
                                                                                                                                 9 Z 7 Z ?
                                                                                  m

       NEF(;- /T  2  6XE 3 "B7
          I  ; EF%$!8; "

                                         hG |bi =
                                                       Z
                                                           dG0 hG| F̂ |G0 ihG0 |ai .
                                                                                                                                 9 Z 7 61?
    l L + 6-.P; N)  6,!2 % hG| F̂ |G0 i 7
     I !8- + 6-.+ $; 6 !#   <9  +   ?
!# 6  ! 2 7                                                                                                ¤
      G,!#;-.)  6EF 6  ; E'P"%`;# !#6-  6"
T + NEF. )*6;! E   Q & A hr| r̂ |r0 i = r δ(r − r0 )
                                                       *7 7RM( ]%  + %6 9 Z 7 61%? ;
d3 r 0
        !8  ! 2 δ  &("X Q 7
hr| p |r 0 i = δ(r − r 0 )(−i}∇r )                 0

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