Задачи по квантовой механике. Часть 2. Корнев А.С. - 63 стр.

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x
mn
x
mn
=
x
0
√
2
0
√
1 0 0 . . .
√
1 0
√
3 0 . . .
0
√
3 0
√
5 . . .
0 0
√
5 0 . . .
. . . . . . . . . . . . . . . . . . . . . . . .
.
¤
ˆ
F = cos θ
Y
lm
(θ, ϕ) l m
hl
0
m
0
|cos θ |lmi = δ
m
0
m
(
s
(l − m + 1)(l + m + 1)
(2l + 1)(2l + 3)
δ
l
0
,l+1
+
+
s
(l − m)(l + m)
(2l − 1)(2l + 1)
δ
l
0
,l−1
)
.
hl + 1 m|cos θ |lmi =
s
(l − m + 1)(l + m + 1)
(2l + 1)(2l + 3)
;
hl − 1 m|cos θ |lmi =
s
(l − m)(l + m)
(2l − 1)(2l + 1)
,
cos θ
¤
z
                                                               ?Z
    Q4 XE         xmn
                                     A
                                                   √                     
                                                0     1 0       0 ...
                                             √           √               
                                              1 0         3    0   . . . 
                                             
                                          x0       √          √          
                                                                          
                                  xmn    =√  0       3 0        5 . . . .
                                           2 0          √               
                                                    0     5 0 . . .     

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                          lm


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                                             (s
                                                     (l − m + 1)(l + m + 1)
          hl0 m0 | cos θ |lmi = δm0 m                                         δl0 ,l+1 +
                                                         (2l + 1)(2l + 3)
                                                                 s
                                                                                                                        9 Z 7 [ ?
                                                                                               )
                                                                    (l − m)(l + m)
                                                              +                        δl0 ,l−1 .
                                                                   (2l − 1)(2l + 1)
a     + 4!8-% ^  *- E VH E 4]-* 6HN
                                                            s
                                                                 (l − m + 1)(l + m + 1)
                               hl + 1 m| cos θ |lmi =                                   ;
                                                                     (2l + 1)(2l + 3)
                                                            s
                                                                 (l − m)(l + m)
                               hl − 1 m| cos θ |lmi =                             ,
                                                                 (2l − 1)(2l + 1)
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     gU4I< E F G 4 G \.8j:lB€5V698 7         cos θ
                                                                                                                               ¤
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