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Quantum Harmonic Oscillator Visualization

Quantum States
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Click to toggle states. Fill shows phase evolution.

Speed
x
Real part
Imaginary part
Probability |ψ|²
Potential V(x)
Individual states

Harmonic Oscillator

The quantum harmonic oscillator models a particle in a parabolic potential well, like a mass on a spring. It's one of the most important quantum systems because many potentials can be approximated as harmonic near their minimum.

Energy levels are evenly spaced:

The wavefunctions involve Hermite polynomials multiplied by a Gaussian envelope, ensuring they decay smoothly at large distances.

Time Evolution:

Each state evolves as . The phasor diagram shows the phase of each state rotating at its energy-dependent rate. Time is measured in ground-state periods (T₀).

Tip: Click on the phasor squares below the main plot to toggle quantum states on and off. Try activating multiple states to see interference effects!