Incident
wave
Scattered
wave
Dipole Antenna—The Movies
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http://www.ee.iastate.edu/~hsiu/movies/dipole.mov link gone
Oscillating (Accelerating) Charge—The Movies
Dr. Rod Cole, UCD-- http://maxwell.ucdavis.edu/~electro/  Oscillating Charge
Two sets of atomic planes in a sodium chloride crystal
Planes in a simple cubic crystal
Many sets of planes to diffract from
In any crystal, some stronger than
others
Protein Structures from X-Ray Diffraction
X-ray beam
Diffracted x-rays
The protein
crystal
X-ray diffraction pattern:
Many spots
Computer
analysis
Structure of
protein/RNA/DNA
Biology
Particles behaving
as waves (de Broglie):
 = h/p
Why a peak and not
continuous as in
Rutherford scattering?
The Davison-Germer Experiment: Details
 decreasing

I(z)=
I(0)exp(-z/e):
Strong
inelastic
scattering
attenuation
A little demonstration of “row” diffraction
with diffraction gratings
Single
diffraction
grating
-1 

1
Double
diffraction
grating
-1,1 
-10 

-1,-1
D
D
D/2
01



0,-1

11
 10
 1,-1

I(z)=
I(0)exp(-z/e):
Strong
inelastic
scattering
attenuation
The experimental
pattern from Ni(111)
Top
Second layer
rows
layer
rows
(attenuated)
The Davison-Germer Experiment: Details Explained
NEUTRONS (AND
OTHER PARTICLES)
DIFFRACT TOO:
deBroglie = h/p
In reactors,
use H2O and
D2O (to avoid
reaction n + p
= d in H2O.
The American Physical Society
looks back to this expt.
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LANDMARKS: ELECTRONS ACT LIKE WAVES
APS has put the entire Physical Review archive online, back to 1893.
Focus Landmarks feature important papers from the archive.
A 1927 paper in the Physical Review demonstrated that particles of
matter can act like waves, just as light waves sometimes behave
like particles. Clinton Davisson and Lester Germer of the Bell
Telephone Laboratories in New Jersey found that electrons scatter
from a crystal in the same way that x rays do. The work began as a
result of a laboratory accident and ultimately earned Davisson a
Nobel Prize.
(C. Davisson and L. H. Germer, Phys. Rev. 30, 705)
Link to the paper: http://link.aps.org/abstract/PR/v30/p705
COMPLETE Focus story at http://focus.aps.org/story/v17/st17
Electron diffraction from a crystal
Davisson & Germer-1925
A particular silicon surface
(1980s)
ELECTRONS AS
DE BROGLIE WAVES
(CONTINUED)-YOUNG’S DOUBLE-SLIT
EXPERIMENT:
L >> D

Maxima when:
Dsin = n
Constructive
Interference or
Superposition

D

Maxima when:
Dsin = 
Constructive
Interference or
Superposition
http://www.walter-fendt.de/ph14e/doubleslit.htm
Don’t know where individual bright spots will appear, but
know probability, proportional to light wave intensity  |Wave|2 = ||2,
and finally, with many individual photon events, see detailed image.
Interference of electrons with a double slit
Just like light on film, with final intensity  |Wave|2 = ||2
But how do we calculate the function of the wave = “wave function ” ?
How well can we measure
the electron position with a photon
(or any scattering de Broglie wave)
With  = h/p?
xsin  /2
Destructive

p0

p
Heisenberg’s Gedanken (Thought) Experiment
(Initially, he forgot the microscope resolution)
A first
“Uncertainty
Principle”
Adding (superposing) stationary waves:
Superposition of traveling waves:
Trig. identity :
cos a  cos b 
1
2 cos (a  b)
2
1
 cos (a  b)
2
E.g.--Musical notes
close together in
frequency
Movies at:
http://galileo.ph
ys.virginia.edu/
classes/109N/m
ore_stuff/Apple
ts/sines/Group
Velocity.html
v group 
v phase

k
d

dk
http://www.colorado.edu/physics/2000/applets/fourier.html
Superposing waves—
Much more general
method
(See additional
reading at website)
kn+1,n = kn+1 – kn = 2(n+1-n)/
= 2/
Ex.—
Does
this
work?
FOURIER (CONT’D..)
Example determination of one of the coefficients an:
?
an 
zero, unless m = n


2  a0
2 m
2 m
2 n
[
a
cos(
x
')
b
sin(
x
')]
cos(
x ')dx '




m
m

 0 2 m 1



m 1
zero
zero
2
2an 
2 2 n
2 2 n
x ')dx ' 
cos (
x ')dx '
  an cos (

 0

 0

and with change of var iable :
2an
2 n
 2 n
2 2 n
cos
(
x
'
)d(
x ')



2 n 0



an 2  n
an
2
cos
(
x
"
)
d


  n  an , just what we want !
x
"

n 0
n
Nice cosine and sine series at: http://www.falstad.com/fourier/index.html
Nice set of variable cosine series at: http://www.falstad.com/fourier/index.html
http://www.physics.ucdavis.edu/Classes/NonclassicalPhysics/FourierTransform/index.html
n=1
0
x

2
bn
0
n=5
0
sines
1
-1
x

2
cosines
1
an
n=11
0

x
0
2
-1
0
5
n
10
Example application:
• Capacitive reactance:
Q(t) = C(t); (t)= maxcos(t)
dQ/dt = I = -maxCsin(t)Imax=maxC
Imax=maxC= max/(C)-1 = max/XC, with
XC=1/(C)

C
?
n+1,n = n+1 – n = 2(n+1-n)/T
= 2/T
Fourier Integrals—Most General
Let period  (or T) , then kn+1,n = 2/ (or n+1,n = 2/T) 0, and we
can include all kn (or m) values, sums become integrals and, in x:
with
Or in t:
Or in both x and t, traveling
waves:
with
vph(k)= /k—”dispersion”
See supplementary reading from Serway et al.
THE RANGE OF TYPES OF WAVE SUPERPOSITION:
Well-defined
position—
All wavelengths
present
Well-defined
wavelength—
All positions
present—wave is
everywhere
A FINITE WAVE PACKET IN TIMEA SECOND UNCERTAINTY PRINCIPLE
Heisenberg’s
Uncertainty
Principles:
p x x   / 2
 py  y   / 2
 pz  z   / 2
E t   / 2
E.g.,
-Lifetimes of states E,
-Frequency spread in
short laser pulses