Download wavefunctions, uncertainty

PH 103
Dr. Cecilia Vogel
Lecture 18
Review
What is quantization?
Photon
Two pieces of evidence:
blackbody radiation
photoelectric effect
Outline
Duality
Wave and particle
Light and matter
REMINDER – EXAM #2 NEXT WED
relativity and quantum
What Is Light, Anyway?
Is light a wave? Or is it a particle?
It diffracts
It interferes
Has polarization
blackbody radiation
photoelectric effect
Compton scattering
Light shows
Light shows
wave properties particle properties
Wave-particle duality:
Light can show wave or particle
properties, depending on the experiment.
Wave-particle Duality
Is light a wave? Or is it a particle?
Light shows
Light shows
wave properties particle properties
when interacting
when
propagating
with other particles
from point A to
point B
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
E  hf
p  h/
E
hc

E
p
c





Matter, e.g. electrons
f  E/h
  h/ p
2
Only for
E  mc
matter

Cue: ‘m’
p  mv

Only for light
Same
eqns
Cue: ‘c’ without ‘m’
Example
What 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/.
2(95eV )
2
1
K  2 mv so v  2 K / m 
6
2
0.511X 10 eV / c
then p  mv  (9.11X10 -31 kg) (5784790m/s )
then   h/p  (6.626X10 Js)/(5.27X 10 kgm/s)
-19
- 24
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 Y(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.
Y
  Y
i

 UY
2
t
2m x
2
2
Wavefunction Interpreted
For light, where the wavefunction (Efield) 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
 Dx = uncertainty in
position
 = spread in positions
where the wave is.
Dx
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
Dp = uncertainty in
momentum
 = spread in ways the wave
moves.
Dp