Physics 2D Quiz #4
Department of Physics, UCSD
Summer Session II  2009
Prof. Pathria
28 August 2009
Some Useful Data
Speed of light:
c = 2.998
×
10
8
m/s
Planck’s constant:
h
= 6.626
×
10

34
J
·
s
Rest mass of an electron:
m
e
= 9.109
×
10

31
kg
= 0
.
511
MeV/c
2
1 eV = 1.602
×
10

19
J
Schr¨odinger wave equation:

¯
h
2
2
m
d
2
ψ
dx
2
+
U
(
x
)
ψ
=
Eψ
Potential energy of a simple
harmonic oscillator:
U
(
x
) =
1
2
Kx
2
=
1
2
mω
2
x
2
Some Useful Formulae
sin
2
x
=
1
2
(1

cos 2
x
)
cos
2
x
=
1
2
(1 + cos 2
x
)
R
∞
0
e

ax
2
dx
=
1
2
p
π
a
R
∞
0
x
2
e

ax
2
dx
=
1
4
p
π
a
3
R
∞
0
x
4
e

ax
2
dx
=
3
8
p
π
a
5
Instructions
Please write your answers in your blue book, and make sure your secret code
number is written on all pages in indelible ink.
1
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View Full Document1. An electron is contained in a onedimensional box of width 0.1 nm.
(a) Draw an energy level diagram for the electron for states up to
n
= 3, and
show
all
the transitions that would eventually get the electron from the
n
= 3 state to the
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 Spring '08
 Hirsch
 Physics, Mass, Light, Uncertainty Principle, Simple Harmonic Oscillator, Department of Physics, Schr¨dinger wave equation

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