(c)
(d) The region beyond L/2 is classically forbidden and so the
probability of finding the particle in this region is very small,
although non-zero.
(e) The wavefunctions will become those for the simple harmonic
oscillator.
11.22 (a)
(b)
(c)
(d)F=−k(xn−xn− 1 ) +k(xn+ 1 −xn)
(e)
CHAPTER 12
12.1
12.2 (a) The ground state is n= 1
(b) The first excited state is n= 2
12.3
12.4
2 0 2 1 058 10
0
0
−=r = =. ×−^10
a
so ra m
ψ
(^200) π 03 0
(^12)
4
1
2
=− 2 /^0
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
−
a
r
a
era
E
hcRh
=− =−.
3
2 15 eV
E
hcRh
=− =−.
2
2 34 eV
E
hcRh
=− =−.
1
2 13 6eV
Vr
e
r
()=
−^2
4 πε 0
−+−+−−+
Z^22
2 1
2
1
2
22 mx
x
k
xx x x
n
nnnnn
d
d
ψ() [( ) ( )]]()ψψnnxEx= ()
ψψ*d αdforthe
2
0
2
2
22
ÅÅ
xxx Nex x
∞∞
−
∫∫() () =
/ gground state
−+=
Z^22
2
2
22 μ
ψψψ
d
dx
x
k
() xx Ex() ()
μ ρρ
()()
=
+
=
+
=
mm
mm
(^12) mm
12
14 14
14 14
7
Δ
Δ
9
Z.
(.
==
×
×
−
2 −
1 054 10
2 1 054 10
34
mx^34
Js
kkg m
ms
)(. )
.
05 10
11 10 10^111
×
− =× −
466 ANSWERS TO PROBLEMS
9781405124362_5_end.qxd 4/29/08 9:17 Page 466