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Physics 137B, Fall 2007
Problem set 6
: more on methods for timedependent problems
Assigned Friday, 12 October. Due
in box
Friday, 19 October.
1. For
t <
0 a spinless particle is in the ground state of a potential “box” with
V
= 0 from
x
= 0
to
x
=
L
, and
V
=
∞
elsewhere. The wavefunction is
ψ
(
t
) =
r
2
L
e

iE
0
t/
¯
h
sin(
πx/L
)
.
(1)
At
t
= 0 the potential suddenly changes from the box potential to a harmonic oscillator potential
centered on
x
=
L/
2: now the Hamiltonian is
H
=
p
2
2
m
+
k
(
x

L/
2)
2
/
2
.
(2)
For time
t >
0, ﬁnd using the sudden approximation (a) the probability that the particle is in the
ground state, and (b) the probability that the particle is in the ﬁrst excited state. Is either of these
nonzero? You may leave any nonzero answer in the form of an integral.
2. Bransden 9.4. The point of this problem is to make you work through the example of a twolevel
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This note was uploaded on 08/01/2008 for the course PHYSICS 137B taught by Professor Moore during the Fall '07 term at University of California, Berkeley.
 Fall '07
 MOORE
 Physics, mechanics

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