Solutions to Homework Problems in UPC Chapter 6
January 22, 2015
1a) To calculate the force constant we employ Eq. 6.5
=
1
=
c
2c
f
m
therefore
f = 4 2 mc2 2
= 4(3.142)2 (1.7 1027 kg)(3 1010 cm/s)2 (3000cm1 )2
N
kg
= 5.4 102 2 = 5.4 102
s
m
b) We can note
Solutions to Homework Problems in UPC Chapter 7
February 4, 2015
1)
2
nx
sin
b
b
n (x) =
|n|2(x)
a) b) From Fig. 1 we can note that for n = 2 the p.d.f. has two lobes each of 1/2 probability, and sin2 (2x/b)
0
0.2
0.4
0.6
0.8
1
x/b
Figure 1: Particle in a
Solutions to Homework Problems in UPC Chapter 8
March 12, 2015
8) Li2+ is a one-electron (hydrogen-like) ion with a nuclear charge of Z=3.
a) We could use Eqs. 8.7 and 8.8 to obtain the appropriate expressions for the radial probability density,
Pnl (r),
Solutions to Homework Problems in UPC Chapter 7
February 26, 2015
14) We need to make use of the fact that [x, px ] = i to prove that [, a ] = 1.
a
Let c = (2m )1/2 , we know that:
and a = c(mx ix )
p
a = c(mx + ix )
p
so,
[, a ] = a a a a = c2 cfw_(mx +
Solutions to Homework Problems in UPC Chapter 7
February 12, 2015
6) The ground state and excited state congurations are shown in the following gure. The LUMO and
n=-2
n=+2
n=-2
n=+2
n=-1
n=+1
n=-1
n=+1
n=0
n=0
Ground State
Excited state
Figure 4: Excitat
Solutions to Homework Problems in UPC Chapter 8
March 6, 2015
1a) The energy is obtained from the formula
En =
hcRH
(6.63 1034 J s)(3.0 108 m/s)(1.0974 107 m1 )
=
n2
n2
En =
2.18 1018 J
n2
and
L2 =
l(l + 1)
The results are summarized in the following ta
Solutions to Homework Problems in UPC Chapter 6
January 28, 2015
2
5) a) (x) = ex , this is a unnormalized wave-function.
1
exp(-x*x)
0.9
0.8
0.7
Psi(x)
0.6
0.5
0.4
0.3
0.2
0.1
0
-2
-1.5
-1
-0.5
0
x
0.5
1
1.5
2
b) The normalization constant is
1
N2 =
1
=
CHM 374
EXAM I
3 February 2016
Name: CPA-7
This exam should have a total of 10 numbered pages,
including the back pages which contain reference material.
Show all your work to receive full credit for each problem. 1) Skin cancer can be caused by the sun t