Lecture 1: Reminder: wave-particle duality

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

Classical “theory of everything”

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

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

Einstein’s explanation: photons 𝛾 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

An explosion in the lab leads to strange results

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):

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?

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: