beyond More pages

From “19. Quantum Mechanics I: The key experiments and wave-particle duality” by YaleCourses

Quantum mechanics: light and electrons as particles and waves

Built up Newton, shot down. Built up Maxwell, going to get shot down.

Open the interactive page →Make a page from any YouTube video

Key points

Light arrives as localized packets, each carrying energy ħω and momentum ħk, as shown by single hits on a very dim photographic film, the photoelectric effect, and Compton scattering. 12:51
Interference shows light is a wave: you add the electric fields of the two paths and then square the sum, because adding the intensities of the two slits gives the wrong answer. 5:48
The wave does not carry energy; its squared height gives the odds of where each photon lands, so the theory predicts only statistics and the pattern appears only after many repetitions. 19:40
Electrons also have a wavelength of h/p and produce interference with two slits, and any attempt to see which slit an electron passes through destroys that interference. 36:48
The uncertainty principle follows from the wave: squeezing a wave to locate a particle makes its momentum spread, so the product of position and momentum uncertainties stays of order ħ. 58:34

Terms

Interference — Waves add their electric fields, so two open slits can cancel in some places and reinforce in others. 5:42
Photon — A massless particle of light carrying energy ħω and momentum ħk, with E = pc. 13:12
Work function — The energy W needed to pull an electron out of a metal. 24:44
Wave function — A function whose squared magnitude gives the odds of finding a particle at a point. 63:01
Uncertainty principle — Localising a particle in position spreads its momentum, so Dx and Dp cannot both be small. 55:23
Planck's constant — The constant h = 6.6 x 10^-34 J s, with ħ = h/2π. 11:48

In order

1. Setting the spirit of the course — The lecturer frames quantum mechanics as hard to follow intuitively, quotes Feynman, and says today Newtonian mechanics and Maxwell's theory will be shot down by new experiments. 0:03
2. Dim light and single photon hits — With a very weak source, a photographic plate records isolated hits, each carrying momentum ħk and energy ħω, so light behaves as particles with E = pc. 6:50
3. Particle or wave: the wave gives odds — The lecturer argues that the wave function sets the probability of where each photon lands, so the answer is neither simply particle nor simply wave. 15:00
4. Compton scattering — Light scattered off an electron shifts in wavelength by an angle-dependent amount, which conservation of energy and momentum explains with photons. 31:20
5. de Broglie waves for electrons — De Broglie proposes electrons have wavelengths, and single electrons in a double slit still build an interference pattern, so they must know how many slits are open. 36:20
6. Wave function and the complex exponential — A particle of definite momentum needs a wave function with constant magnitude, so the lecturer arrives at A e^(ipx/ħ) and a summary of the day's lessons. 59:50

The argument, point by point

Light arriving at a photographic plate in weak intensity shows up as single localised hits. 12:18
A photon's wave is a property of one photon, not of a beam. 20:44
Electrons are assumed to have a wave associated with them, with wavelength 2πħ/p. 36:42
Interacting with a quantum system changes its behaviour, so it has no definite path until seen. 45:24

Chalk marks worth a closer look

Photographic plate behind the slits — Chalk writing reads 'photographic plate' beneath a drawn cylinder of interference fringes.
Planck's constant on the board — Chalk line reads 'h = Planck's' and '6.6 x 10^-34 J s' under the equations for E and p.
E = pc boxed — A boxed equation E = pc sits among the ω = kc and E = ħω relations.
Diffraction condition d sinθ = λ — Chalk shows d sinθ = λ above a diagram of a beam spreading through a slit.
Complex wave function — Chalk writes ψ(x) = A e^(ipx/ħ) with a small phase diagram beside it.

More pages like this

Talks, history and ideas →