Задачи по квантовой механике. Часть 2. Корнев А.С. - 58 стр.

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a
|ai
ha|
ha| = |ai
†
|bi =
ˆ
G |ai, (|bi)
†
= hb| = (
ˆ
G |ai)
†
= (|ai)
†
ˆ
G
†
= ha|
ˆ
G
†
.
|ai |bi
hb| |ai hb|ai
hb|ai = ha |bi
∗
ha|ai = 1
ˆ
G
ˆ
G |G
n
i =
G
n
|G
n
i
hG
n
|G
m
i = δ
G
n
G
m
= δ
nm
.
δ δ
ˆ
F = |biha|
hb|ai
ˆ
F |ci = |biha|ci; hc|
ˆ
F = hc|biha|.
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      ; X Q ] % !#; 2 T  2 A ha| = |ai† 7LM(] % - c N !#%!# 2 
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            ;) 8  ^ /7 7*!8-
                                                     (|bi)† = hb| = (Ĝ |ai)† = (|ai)† Ĝ† = ha| Ĝ† .
                b " N6)   ^ K > i 5fF24MB€> G €> R  F qC 4I>fg;F GR 5V6_>[4I< E < R  E F DE GAK > i 5fF24WBDud R \.BDF G 4 G 5 G R PDNO> EDE=GIHJG G 9> R fg;F G R 5 R [4 G 7
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* hb| |ai A hb |ai 7 @ "O6- 2 >;)# |ai                 2 |bi- 2  ! 2 NEFE  "%% 
    ;O- "O!#E '!8-%'a-  2  !#,6T \c hb |ai = ha |bi∗ 7
             IR "E ^ !# !#!c 5T !# !# 2  2  &(+  OT  2 ^ *L
 %.  !8- ha |ai = 1 7
           > )!#EF  "E -Q+  ] %D;  Ĝ 9 Ĝ |Gni =
                     ? N -  2 .  !8-\c "
                                                                                                                     9Z 70 9 ?
Gn |Gn i


     @ Q!# 9 Z 7 0 9 ? );! >- 2 !#" +  !#; "7 I !8-; EF
                                                 hGn |Gm i = δG G = δnm . n    m



  + L!#; " δ  !#-a)*  2  ! 2 δ  &("XQB7
            C(!#"X 2 F̂ = |biha| ^ T-  hb |ai ^ 2 - 2   ! 2 G €> R  "BA


                        
                                    F̂ |ci = |biha |ci ;

                                                         
                                                                       ,+                8,++
                                                                            hc| F̂ = hc |biha| .
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