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Physics 344
Foundations of 21
st
Century Physics:
Relativity, Quantum Mechanics and
heir Applications
Their Applications
Instructor:
Dr. Mark Haugan
Office:
PHYS 282
[email protected]
TA:
Dan Hartzler
Office:
PHYS 7
[email protected]
Grader:
Shuo Liu
Office:
PHYS 283
[email protected]
Office Hours: If you have questions, just email us to make an
ppointment.
e enjoy talking about physics!
appointment.
We enjoy talking about physics!
Reading: Six Ideas That Shaped Physics Unit Q, Chapters 10 and 11
Notices: Problem Set 11 is due next Monday before the beginning of
ur last lecture session before Thanksgiving
our last lecture session before Thanksgiving
Midterm II at 8:00pm, Thursday, December 2 in MSEE B012
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View Full Document atter Waves
Matter Waves
Last week during recitation we saw evidence that an electron beam with
suitable kinetic energy diffract from crystals in the same way that xrays do.
omparing cases quantitatively reveals that in both cases the wave vector
Comparing cases quantitatively reveals that in both cases the wave vector
associated with the xray photons and with the electrons is related to their
momenta by the deBroglie relation
k
G
G
pk
=
We’ve managed to reconcile the particle and wavelike aspects of photons
by introducing complexvalued representations of the corresponding
electromagnetic fields that we can use to predict probabilities of detecting
photons with different energies and momenta and in different locations at
different times.
In the case of the
y
polarized cavity fields that we have studied most closely,
()
( )
sin(
)
2
nn
n
n
ik x
ik x
it
yn
n
n
n
n
n
ee
Ei
i
k
x
e
i
i
e
i
ω
αβ
−
−−
−
=−
∑∑
^
py
y
,
these probability wave amplitudes are
( )
cos(
)
2
ik x
ik x
zn
n
n
n
n
cB
i
k x e
i
e
−
+
^
We have written them in the final form to emphasize that the fields propagating
()
( )
sin(
)
2
nn
n
n
ik x
ik x
it
yn
n
n
n
n
ee
Ei
i
k
x
e
i
i
e
i
ω
αβ
−
−−
−
=−
∑∑
^
freely within the cavity are plane waves
( )
cos(
)
2
ik x
ik x
zn
n
n
n
n
cB
i
k x e
i
e
−
+
^
hich as you will recall satisfy the wave equation for example in the case
which, as you will recall, satisfy the wave equation, for example, in the case
above
22
2
1
yy
E
E
ct
x
∂∂
=
∂
∂
2
1
zz
BB
x
=
∂
∂
and
The is sufficient to assure that the particles associated with our probability wave
amplitudes have the correct relationship between their energy and momentum
to be photons,
2
2
2
2
2
1
E
=
2
kk
p
cc
c
ω=
⇒==
=
=
However, the electric and magnetic fields together must satisfy Maxwell’s
quations to assure that photons have the correct internal structure (spin).
equations to assure that
photons have the correct internal structure (spin).
The wave equation alone would govern probability amplitudes a hypothetical
structureless photon.
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View Full Document It seems natural to think that we can reconcile the particle and wavelike
behavior of massive particles be taking a similar approach.
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue University.
 Spring '08
 Garfinkel
 mechanics

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