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Quantum & Atomic Physics

Probability Density

The probability per unit volume of finding a quantum particle at a specific spatial position at a given time.

Governing formula P(x) = |ψ(x, t)|² = ψ*(x, t) ψ(x, t)
SI unit m⁻¹ (1D) or m⁻³ (3D)

In depth

Formulated by Max Born, probability density converts the complex amplitude of a wave function into a measurable real probability. Integrating probability density over a spatial volume V yields the numerical probability (0 to 1) of detecting the particle in that region.

Examples in the real world

Mapping electron density clouds in chemistry to identify covalent bonding regions between atoms in molecules.