1. Lecture 1: Reminder: wave-particle duality

2. All physical theories on one slide
Inverse speed of light, 1/c
Special relativity,
Classical
mechanics
Newtonian gravity
Einstein’s
general relativity
Quantum field theory
(Feynman, Dirac, Schwinger,…)
Non-relativistic
quantum mechanics,
(Bohr, Heisenberg, Schrödinger,…)
Mathematicalformalism
(common language)
Theory of everything
(does not exist yet)
Planck’s constant,
Gravity constant, G

3. Classical “theory of everything”

4. The photoelectric effect
Classical theory predicts that increasing
the intensity of the light should lead to
more energetic photoelectrons. Light of
any frequency should be able to kick
electrons out of the metal plate.
Experiment showed exactly the opposite:
1. The energy of electrons did not depend
on the intensity.
2. No photoelectrons were produced if the
frequency was smaller than a critical value. e e e e

5. Einstein’s explanation: photons
“The usual conception that the energy of light is continuously distributed over the space through which it propagates, encounters very serious difficulties when one attempts to explain the photoelectric phenomena, as has been pointed out in Herr Lenard’s pioneering paper.
According to the concept that the incident light consists of energy quanta …, however, one can conceive of the ejection of electrons by light in the following way. Energy quanta penetrate into the surface layer of the body, and their energy is transformed, at least in part, into kinetic energy of electrons. The simplest way to imagine this is that a light quantum delivers its entire energy to a single electron: we shall assume that this is what happens…”
Concerning an Heuristic Point of View Toward
the Emission and Transformation of Light
A. Einstein
Bern, 17 March 1905 e e e e

6. Einstein’s explanation: photons𝛾 𝛾
Einstein’s explanation: photons 𝛾 𝛾
The Nobel Prize in Physics 1921 was
awarded to Albert Einstein "for his
services to Theoretical Physics, and
especially for his discovery of the
law of the photoelectric effect". e e e e

7. An explosion in the lab leads to strange results

8. What did they actually see?
But this is what waves are supposed to do! Davisson (Nobel, 1937) and Germer say in the paper:
“The most striking characteristic of these beams is a one to one correspondence ...which the strongest of them bear to the Laue beams that would be found issuing from the same crystal if the incident beam were a beam of x-rays. Certain others appear to be analogues ... of optical diffraction beams from plane reflection gratings. Because of these similarities ... a description ... in terms of an equivalent wave radiation ... is not only possible, but most simple and natural. This involves the association of a wavelength with the incident electron beam, and this wavelength turns out to be in acceptable agreement with the value h/mv …, Planck's action constant divided by the momentum of the electron.” 
This correspondence was predicted by Prince de Broglie (Nobel, 1929):

9. What’s going on? Summary
We have learned about two Nobel-prize winning works (photoeffect and electron
diffraction) and all in all “met” in passing 6 Nobel laureates in our first lecture
(Michelson, Lorentz, Lenard, Einstein, Davisson, De Broglie)
We have seen that there is clear experimental evidence that light behaves (sometimes)
as a beam of particles carrying energy quanta.
On the other hand, there is also evidence that electrons (sometimes) behave as waves.
What’s going on?

10. What is more fundamental: particles or waves?
Particle has well-defined velocity
and position at any given time.
A sinusoidal wave is characterized by or
It’s hard to represent a wave with particles, but we can decompose a localized particle into waves:
Fourier transform: