The tutor in action
Start learning.
Prof Tong · narrating
"Why does the double-slit experiment make an interference pattern, even with one electron at a time?"
Step 1 · the wavefunction
Each electron travels as a wavefunction ψ(x) — not a single point. After both slits, the total is a sum of two waves:
ψ(x) = ψ₁(x) + ψ₂(x)
Step 2 · what we measure
The probability of finding the electron at position x on the screen is |ψ(x)|²:
|ψ|² = |ψ₁|² + |ψ₂|² + 2 Re(ψ₁* ψ₂)
Step 3 · the punchline
That third term — the cross-term — is the interference. Even one electron, going through alone, interferes with itself.
↳ this is the interference
Sim Studio · Live
Drag to rotate
Just getting started?
Four hand-picked entry points for first-year undergrads. No prerequisites.
Mechanics
Forces, made visible
5 min · Year-1
Thermo
The world's most elegant machine
10 min · Year-2
Modern
Why atoms glow
8 min · Year-1
Waves
Waves are everywhere
7 min · Year-1
4 ways in · books · courses · lectures · wiki
Watch or read.
Books ›
Gravity · 11 chapters
General Relativity
Geometry as gravity
Quantum · 14 chapters
Quantum Mechanics
From amplitude to operator
E&M · 10 chapters
Electrodynamics
The dance of fields
Mechanics · 12 chapters
Architecture of Motion
Newton to Hamilton
All 11 →
Courses ›
In-house · 12 lessons
General Relativity
Prof Rajaram · 28 hours
In-house · 23 lessons
Solid State Basics
After Steve Simon (Oxford)
Graduate · 5 lessons
QFT · Renormalization
After Peskin & Schroeder Ch 10
Forthcoming
Quantum Mechanics
David Tong · Cambridge
All →
Lectures ›
▶ MIT 8.01 · 35 lectures
Walter Lewin · Mechanics
The legendary undergrad course
▶ MIT 8.04 · 26 lectures
Allan Adams · Quantum I
Undergrad QM
▶ Stanford · 10 lectures
L. Susskind · Theoretical Min.
Classical mechanics refresher
▶ DAMTP · 33 lectures
David Tong · QFT
Cambridge Part III
All 28 →
Wiki ›
Mechanics · 7 min
Lagrangian mechanics
Newton's laws in any coords
Relativity · 8 min
Special relativity
From one fact: E = mc²
E&M · 6 min
Maxwell's equations
Four lines, all of light
Quantum · 6 min
Uncertainty principle
Δx · Δp ≥ ℏ/2
Browse all →
5 standalone tools
The full kit.
11 in-house textbooks
248 study guides
1,400 wiki articles
500+ solved problems
22 mock tests
Free, forever.
