Задачи по квантовой механике. Часть 2. Корнев А.С. - 49 стр.

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U(r) =
(
0, r 6 a;
+∞, r > a,
R(r) = R
I
(r) 0 6 r 6 a R(r) = R
II
(r) r > a.
U(r) = ∞ r > a R
II
(r) ≡ 0
0 6 r 6 a U(r) = 0
R
I
(0) = 0 R
I
(a) = 0
R(r)
r = a R
I
(r)
r = a
l
E
nl
=
}
2
X
2
nl
2µa
2
,
X
nl
> 0 n j
l
(x)
j
l
(ka) = J
l+
1
2
Ã
r
2mE
}
2
a
!
= 0.
n = 1, 2, . . . X
nl
X
nl
(n, l)
l = 0 s j
0
(x) =
sin x
x
sin(ka) = 0 ka = πn n = 1, 2, . . .
s
E
ns
=
π}
2
2µa
2
n
2
(n = 1, 2, . . .)
n = 0 ¤
                                                                                             1   m
x(y{z|y{}~€yIM(X/-. 2 ] + 2 TSQa)/S(   A
                                                                                      (
                                                                                           0,               r 6 a;
                                                                   U (r) =
                                                                                           +∞,              r > a,
     /7 7:;- X 6-.!8  7 M(] %`%!#6476\.`#
       9 @7 m ? 7 b "_"O" ; X6-. 2 ] + 2   $) EFEFQ 8%"  ^
       7 6T P%  2 9 7@m ? !8-#!#"O.
                   R(r) = RI (r)
                                            - 2 0 6 r 6 a               R(r) = RII (r)
                                                                                                 - 2 r > a.
                I !8 2 ) _!4 ^  U (r) = ∞ ; r > a ^ R (r) ≡ 0 ^  
         9 =7 m ?  ;N 8 >7 6 6.a4N- !# 0 6 r 6 a ! UII(r) = 0 +E 
 !8- 2 V R (0) = 0 R (a) = 0 7 IR+  !8- ! -# H)
        !#6 E 8 I !8-Q ^  I a)  !8- 2  ; EF%!# R(r) a"%
                    7 I  ) *-./6 - 2 &(%"X R (r) ;-* %  9 7 0 : ? 7  + 
 7 6T PQ  ;  7 Z 7 (AN I8VT-\6T.T;--. ;
r =a
  N%6. ^ NE_N6O- !#.3/-."% r = a 7
                 o\EFQ 8%"  OT  2 !#XE ;* " "%%6Uc
     ] +  *!#"Q8_% Q ^ !# !#! c 5TU8 )*/ % N66-.%
    "%%L!8- l A
                                                         E =
                                                                  }2 Xnl 2
                                                                            ,
                                                                                                                 9 7 Z5 ?
                                           Qa*-. ! &( *!#"%QH&(%"X>R! !#- 2
                                                                                   nl
                                                                                                     2µa2
+      Xnl > 0                     n                                                                                                          jl (x)
                                                                                                                                                             A

                                                                                                                                                                                  9 7 Z0/?
                                                                                           Ãr                         !
                                                                                                      2mE
                                                        jl (ka) = Jl+ 12                                  a                  = 0.
                                                                                                       }2

%!# ! 8  79 a )7 0/0*L? nE 83=) 1,*2, .. Q.  ^ !82 X !#6N!*-c 5TQ8%6R <[E,k[697 BD: EDT  \ ;^ ,!8# ^
  !#;*S c T             5 Q8  /7 b " XN)   ^ !#; X&(!#"% - 2 "*-%!#"%+ (n,H;l)
                                                                                                 nl
                                                                          nl

 X6-   !8-Q  EF/3P3   ! -%(!#!# /7
        I !#%H!8-% l = 0 9 s !#%!8 2  ?8^ EF% 2 ^  j (x) = sin x ^  
 !# 9 7 Z0/? ;-*$%6  sin(ka) = 0 ^ "S ka = 0πn 9 n = x1, 2, . . .? 7
  b + S!#; " s !#%!# 2 Q>   A
                                                                        π}2 2
                                                       Ens =                 n                         (n = 1, 2, . . .)
                                                                        2µa2
9 n = 0 P*-  2   &() *!#"%Q>; !#6"%()**S ? 7                                                                                                   ¤

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