Probability amplitude

A complex number associated with a quantum state or outcome. Its squared modulus gives the probability of that state or outcome.

Born rule: The rule that converts a quantum state's amplitudes into probabilities by taking squared moduli. It specifies how an amplitude becomes a measurable probability.
Quantum state: A mathematical description of a quantum system that determines probabilities for possible measurement outcomes. Amplitudes are components of a quantum state or coefficients for its possible outcomes.
Double-slit experiment: An experiment in which particles passing through two openings produce an interference pattern. The pattern depends on adding the amplitudes for passage through both slits.
Probability: A real number from zero to one quantifying the likelihood of an event. Unlike probabilities, amplitudes are complex and combine linearly before measurement.
Quantum interference: The enhancement or cancellation of quantum probabilities when alternatives combine as amplitudes. Relative phases make amplitudes reinforce or cancel before probabilities are obtained.
Complex number: A number expressible as a real part plus an imaginary part. An amplitude's real and imaginary parts encode magnitude and phase.
Mach–Zehnder interferometer: An optical interferometer that splits light into two paths and recombines them at detectors. Changing a path phase redirects detection probabilities through amplitude interference.
Probability density: A nonnegative function whose integral over a region gives the probability of finding a quantity there. A wavefunction's squared modulus is a density, whereas the wavefunction itself is an amplitude.
Quantum phase: The angle specifying the complex phase of a quantum amplitude. An amplitude's phase can affect interference even though it does not change its individual probability.
Hilbert space: A complete inner-product vector space used to represent quantum states and observables. Quantum amplitudes arise as coordinates and inner products in this state space.

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