Physics 3101,
Introduction to Modern Physics
, Fall 2004
EXAM #2
Monday, November 8, 2004
Instructions
Read each problem carefully before starting. Choose 3 of the following 4 problems.
Remember to work each problem as fully as possible.
Partial credit will be given so
SHOW ALL OF YOUR WORK!!
Constants:
c
= 3 x 10
8
m/s
h
= 6.63 x 10
34
J s =
4.14 x 10
15
eV s
h
=
h/2
π
k
=
0
4
1
πε
=
8.99 x 10
9
N m
2
/C
2
hc
= 1240 eV nm
k =
Boltzmann’s constant = 1.38 x 10
23
J/K = 8.61 x 10
5
eV/K
m
e
= 9.11 x 10
31
kg
1 MeV/c
2
= 1.783 x 10
30
kg
Useful relationships:
)
2
cos
1
(
2
1
sin
2
x
x
−
=
1
1
0
1
2
)...
1
(
!
+
+
−
∞
⋅
⋅
−
⋅
=
=
∫
n
n
ax
n
a
n
n
a
n
dx
e
x
1. Consider a one dimensional infinite square well in which V = 0 in the range 0<x<L.
(a) Assuming that a particle of mass m obeys the Schrodinger equation, write down a
general expression for the normalized wave functions of the well states.
Also
write down an expression for the energies of the well quantum states.
(12 points)
(b) Compute the expectation value
<p
2
>
for the nth wave function.
Using this result,
compute the expectation value
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 Fall '08
 Staff
 Physics, Work, 1 k, 0 k, Pauli, 23 J, 30 kg

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