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
2
2
2
2
2
1
2
2
2
m x
x
k x
k
x
d
d
ψ( )
( )
( ) ψ ψ
ψ
( )
( )
x
E x
=
−
+
+
=
−
Z
2
2
2
2
2m x
x
Ax
Be
x
E x
x
d
d
ψ
ψ
ψ
( ) (
) ( )
( )
ν
ν
ρ
ρ
16
15
8
7
0 97
O
O
/
/
(
)
(
)
.
=
=
k m
k m
μ
ρ
ρ
( )( )
.
=
+
=
15 15
15 15
7 5
m
m
μ
ρ
ρ
( )( )
=
+
+
+
=
m m
m m
m
m
1 2
1
2
16 16
16 16
8
E
m
m
mk
k
m
0
2
2
2
2
1 2
2
2
2
/
=
=
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟ =
⎛
⎝
⎜
Z
Z
Z
Z
α
⎜ ⎜
⎞
⎠
⎟ ⎟ =
1 2
2
/
Zω
−
+ =−
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟ + =
Z
Z
Z
2
4
2
2
2
2
2
2
0
m
k
m
mk
k
α
ψ
α
α
0
2
2
4
2
2
0
2
2
2
( )
x x
m
k
m
E
−
+
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟ +
−
⎛
⎝
Z
Z
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
= 0
−
−
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟ +
Z
2
0
2
4
2
2
2
1
2
m
x
x
k x
ψ
α
α
( )
ψ ψ
ψ
0
0 0
( )
( )
x
E
x
=
=
−
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
( )
ψ
α
α
0
2
4
2
1
x
x
d
d
d
d
2
2
0
0
2
2
0
2
2
x
x
N
x
x e
N
x
ψ
α
α
( )
/
=
−
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟ =
−
e e
x
x
−
−
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
2
2
2
2
4
2
1
/ α
α
α
d
d
d
d
x
x
N
x
e
Ne
x
x
x
ψ
α
α
α
0
0
2
0
2
2
2
2
2
2
( )
/
/
=
=
−
⎛
⎝
−
−
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟
464
ANSWERS TO PROBLEMS
9781405124362_5_end.qxd 4/29/08 9:17 Page 464