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