PH 103

Dr. Cecilia VogelLecture 18

Review

Outline

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

Momentum Uncertainty

A wave is not moving in just one way.

For example sound waves spreading out around the room, light from a bulb,

and yes, matter wave, too p = uncertainty in

momentum = spread in ways the

wave moves.

p