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What is quantization? Photon Two pieces of evidence:
blackbody radiation photoelectric effect
Duality Wave and particle Light and matter
REMINDER – EXAM #2 NEXT WED relativity and quantum
What Is Light, Anyway? Is light a wave?
It diffracts It interferes Has polarization
Light shows wave properties
Or is it a particle? blackbody
radiation photoelectric
effect Compton
scattering
Light shows particle properties
Wave-particle duality: Light can show wave or particle
properties, depending on the experiment.
Wave-particle Duality Is light a wave?
Light shows wave properties when propagating from point A to point B
Or is it a particle?
Light shows particle properties when interacting with other particles
When do We See Which? Two-slit experiment
Light will propagate through both slits and waves through slits interfere with
each other, but when it strikes the screen,
it interacts with the screen one photon at a time.
Matter Matter particles, like electrons,
have particle properties (of course) individual, indivisible particles energy & momentum
Duality of Matter Matter particles, also have wave
properties! They diffract! They interfere! Diffract from a
crystal, interference pattern depends on crystal structure
...from a powder, pattern depends on molecular
structure
http://hyperphysics.phy-astr.gsu.edu/hbase/davger.html#c1
Duality equations Light/photons Matter, e.g.
electrons
/hp
hfE
ph
hEf
/
/
Sameeqns
c
E
hc
p
E
Only for light Cue: ‘c’ without ‘m’
mv
mc 2
p
EOnly for matterCue: ‘m’
ExampleWhat is the wavelength of an
electron which has 95 eV of kinetic energy?Note: K<<moc2, so we can use classical equations.
Note: DO NOT USE E=hc/.
kgm/s)10Js)/(5.27XX10626.6(then
)5784790m/s(kg).11X109( then
/eV10511.0
)95(2/2 so
24-19-
31-
262
21
h/p
mv p
cX
eVmKvmvK
Units tips Use one consistent set of units
SI units OR relativity-friendly units do not mix
explosion hazard!
You know h and c individually also useful: the product hc = 1240 eVnm useful in light eqns
If all else fails, convert everything to SI
Wavefunction For light, the wavefunction is E(x,t)
electric field (and B(x,t) = magnetic field).
For matter the wavefunction is (x,t) like nothing we’ve encountered before.
How does one determine the behavior of the wavefunction? The Schroedinger equation Plays the role of F = ma.
Uxmt
i2
22
2
Wavefunction Interpreted For light, where the wavefunction (E-
field) is large, the light is bright there are lots of photons
For matter particles, where the wavefunction is large there are lots of particles
For an individual photon or matter particle, the wavefunction only tells probability that the particle will be there cannot tell where you will find the particle
When do We See Which? In this demo, For a beam of many particles,
many particles strike the points of constructive interference, where wave is large
Considering a single particle, each particle is likely to strike a point of
constructive interference, where wave is large
Position Uncertainty A wave is not at one
place. For example: water
wave hitting the shore, light wave from a source, and yes, matter wave, too
x = uncertainty in position
= spread in positions where the wave is.
x