Download The buoyant force on an object totally submerged in a fluid depends

Louis de Broglie
If light, which we
thought of as a
wave, behaves as
a particle, then
maybe things we
think of as
particles behave
as
waves…
photo from http://www.aip.org/history/heisenberg/p08.htm
Energy/Frequency and
Momentum/Wavelength Relations for a
Photon
p
E  hf
h

Energy/Frequency and
Momentum/Wavelength Relations for an
Electron/Proton/Apple Pie/Ford Taurus
E
hc

????
What Exactly is Waving?

For a photon...
– electric and magnetic fields
– You can measure them if f is small enough.
– For visible light, you can see that it is a wave
indirectly.

For a massive particle
– You can’t measure them --- even in theory!
– They are complex!
– How do we know that there’s really a wave?
How might I verify that my Ford is
a wave?
Thought Question
Which of the following would be the easiest
particle to use if I wanted to see a matterwave diffraction pattern?
A. A car moving at 100 mph
B. A car moving at 1 mph
C. A 1 MeV electron
D. A 10 eV electron
E. What was the question?
Wavelength of a Ford
h
h
 
p mv
m  3336 lb  1.5 103 kg
v  10 3 m/s
34
  4.4  10 m
Wavelength of a 10 eV Electron
h
h
 
p mv
v  1.88 107 m/s
m  9.11031 kg
  0.39 nm
Davisson and Germer
photo from http://faculty.rmwc.edu/tmichalik/davisson.htm
Cesium Interferometer
f2
f3
p/2
f1
p/2
p
Normalized signal
1
0
-1
-10
-5
0
5
10
15
Rotation rate (x10-5) rad/sec
20
Interference of BEC
C60 Interference
Recent results from Vienna group of Anton Zielinger:
The interfering particle: Buckyballs
Apparatus
Interference fringes!
http://www.quantum.univie.ac.at/
Not only more mass,
but more degrees of
freedom too!
Pure Sine Wave
y=sin(5 x)
Power Spectrum
“Shuttered” Sine Wave
y=sin(5 x)*shutter(x)
Power Spectrum
“Thin” Gaussian
y=exp(-(x/0.2)^2)
Power Spectrum
“Fat” Gaussian
y=exp(-(x/2)^2)
Power Spectrum
Femtosecond Laser Pulse
Et=0=sin(10 x)*exp(-x^2)
Power Spectrum
Uncertainty in a Classical Wave
1
 t 
2
1
 x k 
2
Uncertainty Relations
Classical Wave
Position – Momentum
Energy – Time
Wave-Particle Duality

Things act as wave when propagating
– or, in other words, we use waves to make predictions
as to what we will find when we make our
measurement.

Things act as waves when we measure wavelike properties.

Things act as particles when we measure
particle-like properties

Example: BEC interference --- theorists confused
about “undefined phase”
WHERE CAN YOU FIND TRUTH?
A ride with a tow truck driver
 An article on idiots filled with . . . the word
 Peer reviewers trying to sound smart
 A Buddhist Sunday school teacher

WHERE CAN YOU FIND TRUTH?
"We believe in all truth, no matter to what subject
it may refer. No sect or religious denomination [or,
I may say, no searcher of truth] in the world
possesses a single principle of truth that we do not
accept or that we will reject. We are willing to
receive all truth, from whatever source it may
come; for truth will stand, truth will endure."
-- Joseph F. Smith
What is stuff made
of?
Rutherford’s Experiment
θ
Shooting bullets at jello . . .
Radiating Atoms
Bohr’s Theory
He did not think in terms of waves
 He simply postulated that

– There are orbits in which the electron doesn’t radiate.
– The light released when an electron changes orbits is
a photon with an energy equal to the difference in
energy of the two orbits

He further postulated that the orbits were
circular with quantized angular momentum of 𝑛ℏ
Hydrogen
 1
1 
E photon  Eo  2  2 
n2 
 n1
Eo  13.6 eV
Balmer series—
An electron falls to the n=2 energy
state and a photon is emitted.
n=6
n=5
n=4
n=3
to
to
to
to
n=2
n=2
n=2
n=2
410 nm Violet
434 nm Violet
486 nm Bluegreen
656 nm Red
An electron absorbs a photon and
jumps to a higher energy level.
The green emission line in hydrogen is
a transition from an excited state n=4
to n=2. The red line must be a
transition from ______ to n=2.
A.
B.
C.
D.
E.
n=1
n=2
n=3
n=4
n=5
Which transition in hydrogen gives off the
shortest wavelength (highest energy) of
radiation.
A.
B.
C.
D.
E.
n=2 to n=1
n=3 to n=2
n=6 to n=3
n=8 to n=4
n=100 to n=5
Bohr Theory Successes/Failures
☺
☺
☺
☺
X
X
X
X
Predicts emission and absorption lines of hydrogen and
hydrogen-like ions
Predicts x-ray emissions (Moseley’s law)
Gives an intuitive picture of what goes on in an atom
The correspondence principle is obeyed... sort of
It can’t easily be extended to more complicated atoms
No prediction of rates, linewidths, or line strengths
Fine structure (and hyperfine structure) not accounted for
How do atoms form molecules/solids?
X
Where did it come from? There must be a more general
underlying theory!
☺
It gave hints of a new, underlying theory
Schorodinger’s Idea
 Probability
waves
–Tells the probability of finding a
particle at some particular place at a
particular time.
–The electron is more likely to be
where the amplitude of the wave is
high.
ℏ2 𝑑 2
−
Ψ
2
2𝑚 𝑑𝑥
𝑥, 𝑡 + 𝑉(𝑥)Ψ 𝑥, 𝑡
𝑑
=iℏ Ψ
𝑑𝑡
𝑥, 𝑡
Match the spectrum to the one you
see.
H
He
O
Ne
http://astro.u-strasbg.fr/~koppen/discharge/
http://www.colorado.edu/physics/2000/quantumzone/index.html
http://jersey.uoregon.edu/vlab/elements/Elements.html
Tunneling
Cross-section of a MOSFET transistor gate consisting of a 2 nm thick amorphous silicon oxide layer
between crystalline silicon (top) and polycrystalline silicon (bottom). Individual atomic columns and
dumbbells are clearly visible. The image provides data on the precise location and roughness of the gate
oxide interface, while revealing how the silicon crystal structure is locally affected near the interface.
STM image
http://www.almaden.ibm.com/vis/stm/gallery.html
STM image
http://www.almaden.ibm.com/vis/stm/gallery.html
STM image
http://www.almaden.ibm.com/vis/stm/gallery.html
Postulates of Quantum Mechanics
Every physically-realizable system is described by a
state function ψ that contains all accessible physical
information about the system in that state
 The probability of finding a system within the volume
dv at time t is equal to |ψ|2dv
 Every observable is represented by an operator which
is used to obtain information about the observable
from the state function
 The time evolution of a state function is determined
by Schrödinger’s Equation
