Physics 401  Homework #4
1)
Particleinabox (three points each).
Consider a particle of mass (m) confined in a one
dimensional box between x = 0 and x = L. At t = 0 the state of the system is given by a square
function:
L
x
2
)
(
,
4
3
4
L
x
L
0
)
(
x
, otherwise
a) We wish to write this wavefunction as a sum of energy eigenstates:
n
n
n
x
a
x
)
(
)
(
Calculate the correct set of expansion coefficients {a
n
} for this expression.
b) Suppose that at t = 0 we decide to measure the energy of the system. What is the probability
that the result of the measurement will be
2
2
2
2
9
mL
E
?
c) Suppose that we perform the energy measurement, and that the result of the measurement is, in
fact,
2
2
2
2
9
mL
E
. What will be the new wavefunction for the system after this energy
measurement?
d) Now we let the new wavefunction evolve in time. What will be the fully timedependent
wavefunction,
?
)
,
(
t
x
e) After the energy measurement, will the position probability distribution for the system change
as a function of time, or will it be constant in time? Explain your answer.
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 Fall '11
 HALL
 Mass, Work, Quantum Physics

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