Why does the probability density oscillate even though the well is static?

When two or more energy eigenstates are mixed, cross terms proportional to cos((En - Em)*t) appear in |Psi(x,t)|^2. Each eigenstate alone is stationary, but the interference between two different eigenstates beats at their energy difference, which is exactly what the c1/c2 sliders let you switch on and off.

What does the Measure button actually do?

It draws a definite eigenstate n with the Born-rule probability pn = cn^2 / sum(c^2), then freezes the wave function into that pure state psi_n(x), which is stationary — the density stops beating, showing a real projective measurement rather than an animation trick.

Home▸Quantum Physics▸Quantum Field: Particle-in-a-Box Superposition (2D)

Quantum Field: Particle-in-a-Box Superposition (2D)

2D Canvas companion to Quantum Field: a real superposition of infinite-square-well energy eigenstates with a beating probability density, live expectation-value readouts, and a Born-rule measurement collapse.

Quantum Physics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion replaces the 3D version's decorative particle-cloud field with a real physics engine: a superposition of up to four infinite-square-well energy eigenstates, evolved exactly through Ψ(x,t) = Σₙ cₙψₙ(x)e^−iEₙt, whose cross terms make the probability density genuinely beat over time instead of merely drifting. A Measure button performs an actual Born-rule projective collapse — drawing an eigenstate with probability pₙ = cₙ²/Σcₙ² and freezing the density into that stationary state — so both superposition and measurement are driven by the same formulas a textbook would use.

⚙ Under the hood

2D Canvas particle-in-a-box superposition: exact eigenstate sum Ψ(x,t)=Σcₙψₙ(x)e^(−iEₙt), live normalization/⟨E⟩/⟨x⟩ readouts, and a Born-rule Measure button that collapses the wave function into a single stationary eigenstate.

quantum fieldsuperpositionparticle in a boxwave function collapseborn rule

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install