Particle in a box simulation
Trap a particle between two infinitely high walls and only standing waves that fit a whole number of half-wavelengths survive. That single condition is where quantised energy levels come from.
Interactive, free and runs in your browser. Part of the Quantum Mechanics simulations.
What you will see
The wavefunction rises from the floor of a glass well, coloured by its complex phase so you can watch it evolve in time. Nodes stay fixed, neighbouring lobes always sit on opposite colours, a glowing tube shows where position measurements land, and an energy ladder shows the levels spaced as n².
Try this
- Step n from 1 to 4 and count the nodes: always n − 1.
- Switch to Re(ψ) and watch the lobes swap sign as the phase turns.
- Compare the energy ladder gaps: each is bigger than the last.
Common misconception
The particle is not bouncing between the walls like a ball. In a stationary state |ψ|² does not change with time, and at a node the particle is never found, even though it is found on both sides of it.
Exam-style question
An electron in a one-dimensional box has a ground-state energy of 0.5 eV. What is the energy of the n = 3 state, and what would the ground-state energy be if the box were twice as wide?
Eₙ = n²E₁, so E₃ = 9 × 0.5 eV = 4.5 eV. Since E ∝ 1/L², doubling the width quarters the ground-state energy to 0.125 eV.
Key equations
ψₙ(x) = √(2/L) sin(nπx/L)Eₙ = n²h² / 8mL²
Curriculum
AQA A-level physics, IB Physics HL C.3 and E.1.