Quantum · undergrad

Wavefunction Normalization

The total probability associated with a quantum state must equal one.

Published Apr 26, 2026 · 1 min

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Condition

For a single particle wavefunction,

\int_{\mathbb R^3} |\psi(\mathbf r,t)|^2\,d^3r = 1.

$|\psi|^2$ is a probability density. Normalization makes the probabilistic interpretation consistent.

The noncommutativity measure that organizes quantum observables.

The master equation governing the time evolution of the wavefunction.

The unitary operator that advances a quantum state in time.