PH 216, Problem set 4, Due 4/27
1. A particle of mass
M
is in a onedimensional harmonic oscillator potential
V
1
=
1
2
kx
2
.
(a) It is initially in its ground state. The spring constant is suddenly doubled (
k
→
2
k
) so that the new potential is
V
2
=
kx
2
. The particle’s energy is then measured.
What is the probability for Fnding that particle in the ground state of the new
potential
V
2
?
(b) The spring constant is suddenly doubled as in part (a), so that
V
1
suddenly
becomes
V
2
, but the energy of the particle in the new potential is not measured.
Instead, after a time
T
has elapsed since the doubling of the spring constant, the
spring constant is suddenly restored back to the original value. ±or what values
of
T
would the initial ground state in
V
1
be restored with 100% certainty?
2. An electron is in the
n
= 1 eigenstate of a onedimensional inFnite squarewell potential
which extends from
x
=
−
a/
2to
x
=
a/
2. At
t
= 0 a uniform electric Feld
E
is applied
in the
x
−
direction. It is left on for a time
τ
and then removed. Use timedependent
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 Spring '09
 Mass, 2k, Heisenberg, Timedependent perturbation theory, Heisenberg position operators

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