QUANTUM PHYSICS · INTERACTIVE LAB 65
Particle in a box
Build quantum states inside an infinite well and watch their probability distributions evolve.Re(ψ)Im(ψ)|ψ|²Measurement region
Time0.00 fs
Normalisation1.000000
⟨x⟩0.500 nm
⟨p⟩0.000 ħ/L
⟨E⟩0.376 eV
Region probability50.0%
Position expectation through time
Why energies are discrete
The wave function must be zero at both infinitely high walls. Only standing waves that fit exactly inside the well satisfy these boundary conditions, so only particular energies are allowed.
Stationary and evolving states
An individual energy eigenstate changes phase but keeps the same probability density. A superposition combines several frequencies, producing an evolving interference pattern.
Deterministic probabilities
The Schrödinger equation evolves ψ predictably. Measurement outcomes are probabilistic: position follows |ψ|², while an energy measurement returns one of the selected levels with probability |cₙ|².
Idealised model: This is a one-dimensional infinite square well, not a classical bead bouncing between walls. The state is normalised automatically. Click or drag across the main graph to choose a measurement region.