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28. Consider a harmonically bound electron in 1D with Hamiltonian
H
0
=
1
2
~
ω
(
q
2
+
p
2
), initially in its ground
state. A heavy particle passes through the region at high speed. This heavy particle interacts with the
electron through a weak shortrange interaction that can be approximated by the potential
V
(
t
)=
V
0
δ
(
q
−
x
(
t
)) =
V
0
δ
(
q
−
vt
)
,
where
v
is essentially the velocity of the heavy particle (in dimensionless units of the
oscillator), and
V
0
<<
~
ω
is a constant. Sketch the potential seen by the electron for times
t<
0
,t
=0
,
and
t>
0
.
Find the probability that the electron is left in the
f
rst excited state as a result of this collision.
Sketch this probability as a function of
v
.
29. Consider a particle of mass
m
and charge
e
constrained to move on the circumference of a circle of radius
a
lying in the
xy
plane, initially in its ground state. A weak, timevarying, but spatially uniform electric
f
eld “pulse” is applied of the form
~
E
=
E
0
e
−
τ
2
/
τ
2
ˆ
x
which has its peak at
t
.
In
f
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 463 taught by Professor Paule. during the Fall '10 term at Missouri S&T.
 Fall '10
 PaulE.
 mechanics, Work

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