11.15
The term in the left parentheses is:
so the term on the right-hand side must be zero, yielding
11.16 (a)
(b)
11.17
If B << A, the wavefunctions will be the same as those for the
harmonic oscillator.
11.18
−+++−
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
Z
222
2
2
(^1222)
mx
x
k
x
k
x
d
d
ψ() () ()ψψψ()xEx= ()
−++=−
Z^22
2
2
2 mx
xAxBe xExx
d
d
ψψψ() ( ) () ()
ν
ν
ρ
ρ
16
15
8
7
O 097
O
/
/
()
()
==.
km
km
μ ρρ
()()
=.
+
=
15 15
15 15
mm 75
μ ρρ
()()
=
+
+
+
=
mm
mm
(^12) mm
12
16 16
16 16
8
E
mm
mk k
(^0) m
2
2
2
2
12
22 2
/
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟ =
⎛
⎝
⎜
ZZ
Z
Z
α ⎜⎜
⎞
⎠
⎟⎟ =
12
2
/
Zω
−+=−
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟+=
ZZ
Z
2
4
2
222 m^220
k
m
mk k
α
ψ
(^0) αα
2
2
4
2
()xx 222 m 2 0
k
m
−+ E
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟+−
⎛
⎝
ZZ
⎜⎜⎜
⎞
⎠
⎟⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
= 0
−−
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟+
Z^2
0
2
42
2
2
1
m 2
x
xkx
ψ
αα
() ψψψ 000 ()xEx= ()
=−
⎛
⎝
⎜⎜
⎞
⎠
ψ() ⎟⎟
(^0) αα
2
42
1
x
x
d
d
d
d
2
2 002
2
0
22
x
xN
x
x
ψ eNx
α
()=−⎛ /α
⎝
⎜⎜
⎞
⎠
− ⎟⎟= ee
−x x
−
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
222 2
42
/α^1
αα
d
d
d
x d
xN
x
eNe
xxx
ψ
α
αα
00
2
0
2
2
()==−^22 //^22 ⎛
⎝
−−⎜⎜
⎜
⎞
⎠
⎟⎟
464 ANSWERS TO PROBLEMS
9781405124362_5_end.qxd 4/29/08 9:17 Page 464