Задачи по квантовой механике. Часть 2. Корнев А.С. - 42 стр.

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Ψ
lm
(θ, ϕ) = Y
lm
(θ, ϕ), m = 0, ±1, . . . , ±l.
E
l
=
}
2
2I
l(l + 1)
Y
lm
(θ, ϕ) E
l
2l + 1 l = 0 ¤
µ
E
R
00
−
l(l + 1)
r
2
R + k
2
R = 0.
k
2
= 2µE/}
2
R(r) =
√
rZ(r)
x = kr
x
2
d
2
Z
l
dx
2
+ x
dZ
l
dx
+
"
x
2
−
µ
l +
1
2
2
#
Z
l
= 0.
Ψ
klm
(r) = j
l
(kr)Y
lm
(θ, ϕ).
p L
2
¤
                                                               1%

                     Ψlm (θ, ϕ) = Ylm (θ, ϕ),                               m = 0, ±1, . . . , ±l.
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                                                      }2
                                                 El =    l(l + 1)

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Ylm (θ, ϕ)

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                                                      µ
                                                                                             )
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                                         R00 −
                                                  l(l + 1)
                                                           R + k 2 R = 0.
                                                                                                                9 70 : ?
                                                     r 2

 *!8. k2 = 2µE/}2 7 G,!#;-.)  6T;S!86" R(r) = √rZ(r) !T#
* Q ;*Q x = kr ;*4%  9 7 0 : ? " % Uc
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                                                          "             µ     ¶2 #
                                  2
                                 d Zl     dZl             1
                            x2        + x     + x 2
                                                    − l +                            Zl = 0.
                                 dx2      dx              2
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                                                Ψklm (r) = jl (kr)Ylm (θ, ϕ).
                                                                                                                9 7 0*[ ?
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 ) EF  c! *      2 5 @ > R BD:=> 5fg;BQ\`B -B7                                                        ¤

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