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1
ME 501
Homework #1
Due Friday, September 16, 2011
Prof. Lucht (Email address:
Lucht@purdue.edu
)
Note:
A useful table of integrals in posted on the class website.
1.
Laurendeau, Problem 3.2, p. 147.
2. A particle of mass
m
is constrained to move along the xaxis in the region
0
x
L
.
The normalized wavefunction for the particle is given by
(,)
() ()
s
i
n
e
x
p
,
xt
xTt
L
nx
L
i
t
xL
x
x
L
hn
mL
F
H
I
K
F
H
I
K
2
0
00
8
11
1
2
1
2
2
The uncertainty
B
in the determination of the value of a dynamical variable B is given by
the square root of the variance,
BB
B
2
2
.
For a particle with quantum number
1
3
n
, determine the value of the product
x
p
x
.
Is this result consistent with Heisenberg's
uncertainty principle?
3.
A particle confined along a line between
x
= 0 and
x
=
L
is in a "mixed" quantum state, i.e., a
linear superposition of the eigenstates A and B with quantum numbers
1
3
A
n
and
1
5
B
n
,
respectively.
The normalized wavefunction
x t
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