Задачи по квантовой механике. Часть 2. Корнев А.С. - 52 стр.

UptoLike

Составители: 

Ψ
a
(r) a
r Ψ
a
(r)
a
Ψ
a
(r)
a Ψ
a
(r)
a c
a
(G
n
)
Ψ
a
(r)
Ψ
a
(r) =
X
n
c
a
(G
n
G
n
(r)
Φ
G
n
(r)
ˆ
G
ˆ
GΦ
G
n
= G
n
Φ
G
n
Ψ
a
(r) Ψ
a
(r)
c
a
(G
n
)
c
a
(G
n
) Ψ
a
(r)
Ψ
a
(r) c
a
(G
n
)
c
a
(G
n
) =
Z
Φ
G
n
(r
a
(r) d
3
r.
c
a
(G
n
)
a G |c
a
(G
n
)|
2
G
G
a
ˆ
G
G
n
Ψ
a
(r) =
Z
c
a
(G
G
(r) dG;
                                                            9

 
          Dw                                           D*       

          2€% "bŽ 2 OŒŽ}Œ( Œ  Ž  
          *S -Q &("X Ψ (r) 9  a  N'" E 8 !#- ? 
  "%&(+ %6X%`; !#!#.1 "%6 r \+  Ψ (r)3  2 
- 2  ! 2 8!# E  7)3o "*!#" - 2 K < E=EDGIHJG !# !# 2  2 !#!5T!# E 
                                                        a


 2 - 2  ! 2 -\6\.WNa"%6E >   8 !#- a 9  "!\!8%!# 2  2 ? 7 @ $3
                                                                                                     a


   W-QL&("X Ψ (r)   ;#S!#66- 2   !#NQ3-U6T.   
    *!#"%T) N6T   a +  !#%!# 2  2  a 7SI *!# Ψ (r) - 2 ;O
 !  2 !#%!# 2  2  a /LP!#;-.)  6.("%]&,&(X E c (G     a
                                                                                                    )-/T
 2 Ψ (r)                                                                                   a   n)
            a
                                       Ψ (r) =
                                                     X
                                                           c (G )Φ (r)
                                                                                                             9 Z 7 0/?
; G 6 EDGYi !#!8*P!#N !# E 8 &(n%"XQ Φ (r) 69u XYGIHJG ] % ; 6
                                          a                     a   n    Gn



  Ĝ 9 ĜΦ = G Φ ?8^  Q!#!c 5\ +   GF G \ NO> R€G 5fF R < E 5fF24?>#^  "
  % ;#G-E &(n %G"X Ψ (r) 7Ul  ! -#  )+  ^ 3  Ψ (r)
                                                                         n




                                                      !) #!5T*!8 T)*63*) P!#a
                     n                n

    >6N% "%]&,&(X  c (G   a

    !#A)*/  c (G ) a) n*\;#- 2  Ψ (r) ;&(*-9 Z 7 0/? ^
    3)  Ψ (r) ;)a- 2 n 3Q 4?5[> c (G ) A                  a
                 a                                              a    n


                                    ca (Gn ) =
                                                    Z
                                                        Φ∗Gn (r)Ψa (r) d3 r.
                                                                                                                9 Z 7 ?
            ; 2  EFQ N c (G ) ) EF  ! 2 -Q'&(%"X Q$!#%!#
2  2  a  G R > K 5 F| E B=aB 7 nIR#- |c (G )|2 9</7 7F" / **- 2
   -Qa&("Xa G ;# !#6-  ?  3a n!8;#- P  2 %!# Q
    )-E 8L) * QW-E G !#%!8 2  ^ 8") *% N 
  "%E 8 !#-  a 7
             4   ^ 4 !# !#"O)3)#*!#.`!8;#-W- 2 ;  Ĝ "6"
      ! !#"E  ^ 6" $!L ; EFE  !#; "  7 I ;%! -# ! -% G
 2 - 2  ! 2  ;EFQ -Q ^ \!#  >9 Z 7 0/? )*  2  ! 2 n
      + %* A

                                      Ψa (r) =
                                                    Z
                                                        ca (G)ΦG (r) dG;
                                                                                                                9 Z 7Z ?