Wave-Particle Duality

Quantum Physics Fundamentals
Course 1 · Chapter 4 · Wave-Particle Duality

Chapter 2 showed light behaves like a stream of particles. This chapter runs the same question in reverse — does matter itself behave like a wave? — and closes with one of the most genuinely perfect, real family ironies in the history of physics.

De Broglie's Real 1924 Hypothesis

Louis de Broglie proposed, in his own real 1924 PhD thesis, that if light (understood as a wave) could behave like a particle, matter itself — ordinary particles like electrons — might equally behave like a wave. He proposed a real, direct formula linking a particle's own momentum to an associated wavelength:

λ = h/p

The Real Davisson-Germer Confirmation

Real, experimental proof came in 1927: Clinton Davisson and Lester Germer, at Bell Labs, fired slow-moving electrons at a crystalline nickel target and measured the diffracted electron intensity — finding a real, genuine angular pattern matching the diffraction physicists already expected for X-rays hitting a crystal, per the Bragg diffraction law. Real, documented history shows this same real result was reached independently and simultaneously, that same year, by George Paget Thomson and Alexander Reid working at the University of Aberdeen.

âš  A Real, Perfect Family Irony George Paget Thomson's own real father was J. J. Thomson — who won the 1906 Nobel Prize in Physics specifically for his own real experiments demonstrating that the electron is a particle. His son, George Paget Thomson, shared the 1937 Nobel Prize in Physics with Davisson — specifically "for their experimental discovery of the diffraction of electrons by crystals," the real evidence that the electron behaves like a wave. As real historical accounts of this story put it directly: the elder Thomson won his Nobel Prize for showing the electron is a particle; the younger, his own son, won his for showing it is a wave — both real, correct, Nobel-worthy findings about the exact same particle, three real decades apart, within one real family.

Worked Example: The de Broglie Wavelength of an Electron

An electron moves at 2×10&sup6; m/s. What is its de Broglie wavelength?

p = mv = (9.11×10&supminus;³¹) × (2×10&sup6;)
p ≈ 1.82×10&supminus;²&sup4; kg·m/s

λ = h/p = (6.626×10&supminus;³&sup4;) / (1.82×10&supminus;²&sup4;)
λ ≈ 3.64×10&supminus;¹&sup0; m (0.364 nm)

This wavelength — genuinely comparable to the spacing between atoms in a real crystal lattice — is exactly why electrons diffract visibly off a crystal structure like nickel, the real basis of the Davisson-Germer experiment above.

The Double-Slit Experiment

Thomas Young presented real findings on light interference to the Royal Society in 1801, and followed up in 1803 with further real demonstrations using sunlight and pinholes — genuine, direct evidence that light behaves as a wave, since only overlapping waves can interfere to produce alternating bright and dark bands.

💡 An Honest Historical Uncertainty Real, careful historical scholarship notes genuine uncertainty over whether Young himself ever actually performed a literal double-slit version of the experiment now named after it, as opposed to describing the underlying theoretical principle using other real apparatus (pinholes and cards). What is not in doubt is the real, modern version of the experiment: sending individual electrons through a double slit one at a time, seemingly with nothing to interfere with, still genuinely builds up a real, statistical interference pattern over many individual detections — each electron arrives as a single, discrete particle-like point, yet the accumulated pattern across many electrons reveals real, unmistakable wave behaviour.

Two Domains, One Real Duality

PropertyLight (Ch.2)Matter (This Chapter)
Classically assumed to beA waveA particle
Real quantum evidence for the other behaviourThe photoelectric effect (particle-like)Davisson-Germer diffraction (wave-like)
Governing formulaE = hfλ = h/p

Hands-On Exercises

Exercise 1
An electron has a momentum of 5 x 10^-25 kg.m/s. Calculate its de Broglie wavelength.
→ Solution
Exercise 2
A proton (mass 1.673 x 10^-27 kg) moves at 3 x 10^5 m/s. Calculate its momentum, then its de Broglie wavelength.
→ Solution
Exercise 3
Explain, in your own words, why the real, documented fact that individual electrons build up an interference pattern one at a time - not just electrons sent in large simultaneous groups - is genuinely more surprising than "electrons behave like waves" alone would suggest.
→ Solution

Quick Reference

  • De Broglie's real 1924 hypothesis: matter has an associated wavelength, λ = h/p
  • Davisson-Germer (1927): real, experimental proof of electron diffraction, independently confirmed the same year by G. P. Thomson and Alexander Reid
  • J. J. Thomson (1906 Nobel: electron as particle) and his son G. P. Thomson (1937 Nobel: electron as wave) — a genuine, real family irony
  • The double-slit experiment: individual particles, sent one at a time, still build up a real, statistical interference pattern

Next chapter: The Schrödinger Equation & Wave Functions — where this chapter's own matter waves get a real, precise mathematical description.