A Particle in a Box

Where energy levels come from

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Confined waves form standing waves: $E_n = \frac{n^2h^2}{8mL^2}$.
• State n has n − 1 nodes; energy grows like n².
• Smaller boxes mean bigger energies: quantum dots change colour with size.

Steps

1. Standing waves
2. Waves in the box
3. A superposition sloshes
4. Climbing the ladder
5. A nanometre box
6. Quantum dots
7. Never at rest