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⚗️ Quantum Harmonic Oscillator Eigenstates (2D)

Interactive 2D Canvas plot of the quantum harmonic oscillator eigenstates ψₙ(x), built from Hermite polynomials and a Gaussian envelope. Animate time evolution, overlay superpositions of two states, and read off energy levels Eₙ = ℏω(n+½).

Quantum Physics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryQuantum Physics

RenderingCanvas 2D

DifficultyModerate

Target FPS60

Controlsn slider selects the quantum number (0-10), ω slider sets the angular frequency (0.5-3), Show all n ≤ 5 button overlays every energy level and its eigenstate, Show |ψ|² button toggles between the wavefunction and the probability density, ▶ Time evolution button animates the stationary-state phase e^(-iEₙt), Superposition (n, n+1) button overlays an equal-weight two-state superposition to show the quantum beat

quantum mechanicswavefunctionHermite polynomialsenergy levelsSchrodinger equationcanvas2d

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⚙ Under the hood

A 2D canvas plot of the quantum harmonic oscillator's stationary eigenstates psi_n(x), each built from a Hermite polynomial multiplied by a Gaussian envelope via a stable recurrence relation. Adjust the quantum number n and angular frequency omega, toggle the probability density |psi|^2, animate the stationary-state phase e^(-iE_n t), or overlay a superposition of two adjacent states to watch a quantum beat at frequency (E_(n+1)-E_n)/hbar.

quantum mechanicswavefunctionHermite polynomialsenergy levelsSchrodinger equationcanvas2d

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