(c)
9.21 (a)
(b)
(c)
9.22 (a)
(b)
(c)
9.23 (a)−iZ∇
(b)x
(c) (−iZ∇)^2 =−Z^2 ∇^2
9.24 (a)
(b)
(c)
9.25 (a)
(b)
(c)
9.26 (a)
=Eψ(x,y,z)
−++
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
Z^22
2
2
2
2
2 mx y z^2 xyz
∂
∂
∂
∂
∂
∂
ψ(),, ++++()()Ax By Czψx y z,,
−+
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟ +
Z^22
2
2
2 mx y^2 xy Axy x
∂
∂
∂
∂
ψψ()( )(,,,,yExy)()= ψ
−+
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟ ++
Z^22
2
2
2 mx y^2 xy Ax By
∂
∂
∂
∂
ψ()(,^33 )( )ψψxy,,=E xy( )
−+
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟ ++
Z^22
2
2
2
3
2 mx y
xy Ax B
∂
∂
∂
∂
ψ()(, yyxy Exy)( )ψψ,,= ( )
−++=
Z^22
2
2
2 mx
xAxBxxEx
d
d
ψψψ() ( ) () ()
−+=
Z^22
2
2
2 mx
xAxxEx
d
d
ψψψ() ( ) () ()
−+=
Z^22
2 mx^2 xAxxEx
d
d
ψψψ() ( ) () ()
Δ
Δ
x
m
.
()(
==
×
×
−
−
Z
2 9
105 10
2 5 10 10
34
3
Js
kg −−−
=×−
61
11 10^26
ms
m
)
.
Δ
Δ
x
m
.
()(
==
×
×
−
−
Z
2 9
105 10
2 5 10 10
34
3
Js
kg −−−
=×−
21
11 10^30
ms
m
)
.
Δ
Δ
x
m
.
()(
==
×
×
−
−
Z
2 9
105 10
2 5 10 10
34
3
Js
kg −−−
=×−
11
11 10^31
ms
m
)
.
Δ
Δ
x
m
.
(.
==
×
×
−
−
Z
2 9
105 10
2 9 11 10
34
31
Js
kg))( )
.
10
−− 71 =576 3
ms
m
Δ
Δ
x
m
.
(.
==
×
×
−
−
Z
2 9
105 10
2 9 11 10
34
31
Js
kg))( )
,
10
−− 10 1 =576 300
ms
m
Δ
Δ
x
m
.
(.
==
×
×
−
−
Z
2 9
105 10
2 9 11 10
34
31
Js
kg))( )
,
10
−− 91 =57 630
ms
m
Δ
Δ
x
m
.
(.
==
×
×
−
−
Z
2 9
105 10
2 1 67 10
34
27
Js
kg))( )
.
10
−− 71 =0 314
ms
m
ANSWERS TO PROBLEMS 457
9781405124362_5_end.qxd 4/29/08 9:17 Page 457