Is this good for educators?

Yes — this version of "Quantum Harmonic Oscillator for a quantum dot" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.

Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Educators · Quantum Harmonic Oscillator

Quantum Harmonic Oscillator for a quantum dot

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a quantum dot live below — adjust the inputs and watch it respond, right in your browser.

Quantum Harmonic OscillatorLive

evenly-spaced energy ladder

Controls

Presets

Quantum number n

Show probability density

The quantum harmonic oscillator — a particle in a parabolic well — has energy levels evenly spaced by ħω, starting at a nonzero zero-point energy of ½ħω. Its wavefunctions are Hermite polynomials times a Gaussian. It models molecular vibrations, phonons, and quantum fields, making it the most important solvable system in physics.

▶ Run in Python

Data Inspector

Energy3.5 ħω

Level n3

Zero-point½ ħω

Governing equation

E_{3} = (3 + \frac{1}{2}) ℏ ω = 3.5 ℏ ω, ψ_{3} (x) \propto H_{3} (x) e^{- x^{2} /2}

Reading this result: State n=3 sits at 3.5 ħω with 3 nodes; levels stay evenly spaced by exactly ħω all the way up the ladder.

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Frequently asked questions

Is this good for educators?: Yes — this version of "Quantum Harmonic Oscillator for a quantum dot" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.