Louis de BroglieIf 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

hfE h

p

Energy/Frequency and Momentum/Wavelength Relations for

an Electron/Proton/Apple Pie/Ford Taurus

????hc

E

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 QuestionWhich of the following would be the easiest particle to use if I wanted to see a matter-wave diffraction pattern?

A.A car moving at 100 mphB.A car moving at 1 mphC.A 1 MeV electronD.A 10 eV electronE. What was the question?

Wavelength of a Ford

mv

h

p

h

kg 105.1 lb 3336 3mv m/s 10 3

m 104.4 34

Wavelength of a 10 eV Electron

mv

h

p

h kg 101.9 31m

v m/s 1088.1 7 nm 39.0

Davisson and Germer

photo from http://faculty.rmwc.edu/tmichalik/davisson.htm

Cesium Interferometer

Rotation rate (x10-5) rad/sec

-10 -5 0 5 10 15 20

Norm

aliz

ed s

ignal

-1

0

1

/2

/2

2

1

3

Interference of BEC

C60 Interference

Interference fringes!

The interfering particle: Buckyballs

Apparatus

http://www.quantum.univie.ac.at/

Recent results from Vienna group of Anton Zielinger:

Not only more mass,but more degrees offreedom too!

Pure Sine Wavey=sin(5 x) Power Spectrum

“Shuttered” Sine Wavey=sin(5 x)*shutter(x) Power Spectrum

“Thin” Gaussiany=exp(-(x/0.2)^2) Power Spectrum

“Fat” Gaussiany=exp(-(x/2)^2) Power Spectrum

Femtosecond Laser PulseEt=0=sin(10 x)*exp(-x^2) Power Spectrum

Uncertainty in a Classical Wave

2

1 t

2

1 kx

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 wave-like 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

Hydrogen

eVE

nnEE

o

ophoton

6.13

1122

21

Balmer series—An electron falls to the n=2 energy state and a photon is emitted.

n=6 to n=2 410 nm Violetn=5 to n=2 434 nm Violetn=4 to n=2 486 nm Bluegreenn=3 to n=2 656 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. n=1 B. n=2C. n=3D. n=4E. n=5

Which transition in hydrogen gives off the shortest wavelength (highest energy) of radiation.

A. n=2 to n=1 B. n=3 to n=2C. n=6 to n=3D. n=8 to n=4E. n=100 to n=5

Bohr Theory Successes/Failures☺ 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

X It can’t easily be extended to more complicated atomsX No prediction of rates, linewidths, or line strengthsX Fine structure (and hyperfine structure) not accounted forX 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 IdeaProbability 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.

=i

Match the spectrum to the one you see.

H HeONe

http://jersey.uoregon.edu/vlab/elements/Elements.html

http://www.colorado.edu/physics/2000/quantumzone/index.html

http://astro.u-strasbg.fr/~koppen/discharge/

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. (Source: FEI Co.)

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