Wave function collapse
lastmod 2026-01-19created 2026-01-191 edits
In quantum mechanics, wave function collapse occurs when a wave function, initially in a superposition of several eigenstates, reduces to a single eigenstate due to interaction with the external world. This interaction is called observation, and it is the essence of a quantum-mechanical measurement, which connects the wave function with classical observables such as position and momentum. Collapse is one of two processes by which quantum systems evolve in time; the other is the continuous evolution governed by the Schrödinger equation. Collapse is a black box for a thermodynamically irreversible interaction with a classical environment.
Calculations of quantum decoherence show that when a quantum system interacts with the environment, the superposition becomes a sum of classical alternatives. Significantly, the combined wave function of the system and environment continues to obey the Schrödinger equation throughout this apparent collapse. More importantly, decoherence is not sufficient to explain actual wave function collapse, because it does not reduce to a single eigenstate.
Before collapsing, the wave function can be normalized into a square-integrable function, and so it is related to the probability density of the quantum-mechanical system. This function can be expressed as a linear combination of the eigenstates of an observable. Observables represent classical dynamical variables, and when one is measured by a classical observer, the wave function is projected onto a random eigenstate of that observable. The observer simultaneously measures the classical value of the observable as the eigenvalue of the final state.