For K-12 Students · Quantum Harmonic Oscillator
Quantum Harmonic Oscillator for a superconductor
Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a superconductor live below — adjust the inputs and watch it respond, right in your browser.
Quantum Harmonic OscillatorLive
evenly-spaced energy ladder
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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.
Data Inspector
Energy3.5 ħω
Level n3
Zero-point½ ħω
Governing equation
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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More with Quantum Harmonic Oscillator
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Frequently asked questions
- Is this good for k-12 students?
- Yes — this version of "Quantum Harmonic Oscillator for a superconductor" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.