PHY4221
Quantum Mechanics I
Fall term of 2004
Problem Set No.3
(Due on November 1, 2004)
1. A particle of mass
m
is in the ground state of the in
fi
nite square well. Suddenly
the well expands to twice its original size – the right wall moving from
L
to
2
L
– leaving the wave function (momentarily) undisturbed. The energy of the
particle is now measured.
(a) What is the most probable result? What is the probability of getting that
result?
(b) What is the
next
most probable result, and what is its probability?
(c) What is the
expectation value
of the energy?
Hint
: If you
fi
nd yourself
confronted with an in
fi
nite series, try another method.
2. What are the energy levels and the eigenfunctions for a potential of the form
V
(
x
) =
(
∞
,
for
x
≤
0
1
2
mω
2
x
2
,
for
x >
0
.
Hint
: This requires some careful thought, but very little actual computation.
3. Solve the timeindependent Schrodinger equation for a centered in
fi
nite square
well with a deltafunction barrier in the middle:
V
(
x
) =
(
αδ
(
x
)
,
for

x

≤
L
∞
,
for

x

≥
L
.
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 Spring '11
 CFLO
 Mass, wave function, ground state

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