How do I simulate a Bloch sphere?

Open this page and use the live Quantum Harmonic Oscillator 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 Bloch sphere from your own measurements.

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Quantum Harmonic Oscillator for a Bloch sphere

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

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

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.

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 Harmonic Oscillator tool models a Bloch sphere 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 Harmonic Oscillator

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

Other ways to simulate a Bloch sphere

Particle in a Box for a Bloch sphere Quantum Tunneling for a Bloch sphere Bloch Sphere for a Bloch sphere Hydrogen Orbitals for a Bloch sphere Special Relativity for a Bloch sphere Photoelectric Effect for a Bloch sphere

Frequently asked questions

How do I simulate a Bloch sphere?: Open this page and use the live Quantum Harmonic Oscillator 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 Bloch sphere from your own measurements.