How do I simulate a harmonic oscillator?

Open this page and use the live Quantum Tunneling tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a harmonic oscillator from your own measurements.

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Quantum Tunneling for a harmonic oscillator

Simulate a harmonic oscillator live in your browser. This runs the real Quantum Tunneling solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

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Quantum TunnelingLive

through a barrier it cannot climb

Controls

Presets

Particle energy E (eV)

Barrier height V (eV)

Barrier width (nm)

Classically a particle with less energy than a barrier is trapped. Quantum mechanically its wavefunction decays inside the barrier but does not vanish, so there is a finite chance it appears on the other side — tunneling. The probability falls off exponentially with barrier width and height, the principle behind scanning tunneling microscopes and nuclear fusion.

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Data Inspector

Transmission T2.34e-6

Reflection R1.000

Regimetunneling

Governing equation

T \approx e^{- 2 κa} = 2.34 e - 6, κ = \frac{2 m ( V - E )}{ℏ} = \frac{2 m ( 5.0 - 3.0 )}{ℏ}, a = 0.50 nm

Reading this result: The barrier is thick and tall relative to the energy, so transmission is vanishingly small — essentially nothing gets through.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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About this simulation

The full Quantum Tunneling tool models a harmonic oscillator with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

More you can do with Quantum Tunneling

Quantum Tunneling for a hydrogen atom Quantum Tunneling for a quantum well Quantum Tunneling for a qubit Quantum Tunneling for the double-slit experiment Quantum Tunneling for a particle in a box Quantum Tunneling for a tunneling electron Quantum Tunneling for a spin measurement Quantum Tunneling for a laser cavity

Other ways to simulate a harmonic oscillator

Particle in a Box for a harmonic oscillator Bloch Sphere for a harmonic oscillator Hydrogen Orbitals for a harmonic oscillator Special Relativity for a harmonic oscillator Photoelectric Effect for a harmonic oscillator Quantum Harmonic Oscillator for a harmonic oscillator

Frequently asked questions

How do I simulate a harmonic oscillator?: Open this page and use the live Quantum Tunneling tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a harmonic oscillator from your own measurements.