Задачи по квантовой механике. Часть 2. Корнев А.С. - 67 стр.

UptoLike

Составители: 

¤
ˆ
A
ˆ
B
G
hG
n
0
|
ˆ
A
ˆ
B |G
n
i
hG
n
0
|
ˆ
A
ˆ
B |G
n
i = hG
n
0
|
ˆ
A
ˆ
1
ˆ
B |G
n
i = hG
n
0
|
ˆ
A
X
n
00
|G
n
00
ihG
n
00
|
ˆ
B |G
n
i.
hG
n
0
|
ˆ
A
ˆ
B |G
n
i =
X
n
00
hG
n
0
|
ˆ
A |G
n
00
ihG
n
00
|
ˆ
B |G
n
i,
¤
a
hn|x |ni =
1
2
a
hn
0
|x |ni =
a
π
2
(
(1)
n
0
n
1
(n
0
n)
2
(1)
n
0
+n
1
(n
0
+ n)
2
)
n, n
0
= 1, 2, . . . n 6= n
0
ˆ
F = cos ϕ
hm
0
|cos ϕ |mi =
1
2
(δ
m
0
,m+1
+ δ
m
0
,m1
)
hm ± 1|cos ϕ |mi =
1
2
x
2
m ω
hn ± 2|x
2
|ni =
x
2
0
2
p
(n + 1 ± 1)(n ± 1) hn|x
2
|ni = x
2
0
µ
n +
1
2
n =
0, 1, . . . x
2
0
= }/mω
                                                            ?:
C(*- !#"Q>; X6-H;*-.%!#%';#S!86-a8+ 6- B7                      ¤
f+(*,+ V G #!G             W< F R DB : =E T > {d 6_>V\ > E F T G 9> R  K 5fF2 E B=B Blk?4I>[5fF EDT n < i F B hGn | ÂB̂ |Gn i n
                                                                                                Â             B̂           G

                                                                          ?
x(y{z|y{}~€yI I !#;% 2 %!8-(;-E 9 Z 7 0 ? ^  * A
                                                                  0




                                                                               X
          hGn0 | ÂB̂ |Gn i = hGn0 | Â1̂B̂ |Gn i = hGn0 | Â                         |Gn00 ihGn00 | B̂ |Gn i .
G(6" ^
                                                                                n00


                       hG | ÂB̂ |Gn i =
                                                     X
                                                          hGn0 | Â |Gn00 ihGn00 | B̂ |Gn i ,
                                                                                                                      9 Z 7 Z1?
 !# !# NEF% ;nO- ;*/T  2  6X 7 o\*-
                           n0
                                                     00


  9 Z 7 Z61? !#;#-%4 - 2  ; EF   2 c 5TU8%! 2  "O!# !# !# 2  2
 ;a] % !# %()*  2  ! 2 + %* 7                          ¤

   "%`"/%#_'VŒŒ"#v&Ž2ŒaŒ*2"!DŽ #
 V)V G ,Q ; "% E  ] + !#"%%H;8S!#6-  ; N%) O
!#W!#XE N*!#"% Q>; 2 + -.Q ; X6-.Q 2  T 6 E a 7
   9 F24?>fF A hn| x |ni = 1 a hn | x |ni = a (−1) − 1 − (−1) − 1
                                                                 (                                             )
                                                                                n0 −n                         n0 +n
                                                 0
                                     2                            π2          (n0 − n)2              (n0 + n)2
                                     ?7
VG
n, n0 = 1, 2, . . . n 6= n0
          ,Q ;                           <9  ;- 2 E 8 "%6 8 ?  ]  
+  *!8"  ;#S!86- ; N%)!# ;-%!#"%+  67 9 F24I>fF A
                                          F̂ = cos ϕ

                           1
hm0 | cos ϕ |mi = (δm ,m+1 + δm ,m−1 )
                                                                ^ O- hm ± 1| cos ϕ |mi = 1 7 ?
  VK3G ,Q ]  2+ *!#"% ;8S!#6-  ;  x2 ; 2N%)!# -
                                     0               0




  Q+  +*!#"%+  %!#X-- 2  !  ! !#Q m !#Q ω 7 9, F^C
   4I>fF A hn ± 2| x2 |ni = x20 p(n + 1 ± 1)(n ± 1) hn| x2 |ni = x2 n + 1 n =
                                                                                              µ          ¶
                                                                                            0
                 2
0, 1, . . . x = }/mω
                                ? 7  2                                                                 2


      “         Œ $# 229% -Ž                         Žb %.-' \                             2
                0

                                                                                                           +"/
             2  &  /2Ž
                                                                                                                                




       M   8  4+ H;8S!#6-  2 " %+ % )*+   a -
        (
E 84&(%"XQ``; 7   )*E  ^ "% ^ %!#6c  ! 2 !8-#!c 5T
 -E_4!#e 6T  2 A