Quantum Systems — Interactive Wavefunction Visualization

System 01

Infinite Potential Well

Governing equations

ψ_{n} (x) = \sqrt{\frac{2}{L}} \sin (\frac{n π x}{L})

E_{n} = \frac{n^{2} π^{2} ℏ^{2}}{2 m L^{2}}

The interactive model uses ℏ = 1.

Amplitude can be positive or negative.

Higher curve values indicate greater detection probability density.

|ψ|²

Increasing n adds nodes and shortens the wavelength inside the well.

Increasing L spreads the state across a wider region and lowers the energy.

Increasing m lowers the energy because the kinetic term becomes smaller.

Governing equations

E_{n} = ℏ ω (n + \frac{1}{2})

ψ_{n} (x) \propto H_{n} (u) e^{- u^{2} / 2}

Here u = √(mω/ℏ) x; the interactive model uses ℏ = 1.

Higher states develop more nodes and oscillations.

Classically forbidden regions remain visible through the quantum tails.

|ψ|²