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Concept
Wave function collapse
Summary
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 an observation, and is the essence of a measurement in quantum mechanics, which connects the wave function with classical observables such as position and momentum. Collapse is one of the 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 superpositions apparently reduce to mixtures of classical alternatives. Significantly, the combined wave function of the system and environment continue to obey the Schrödinger equation throughout this apparent collapse. More importantly, this is not enough to explain actual wave function collapse, as decoherence does not reduce it to a single eigenstate.
Historically, Werner Heisenberg was the first to use the idea of wave function reduction to explain quantum measurement.
Before collapsing, the wave function may be any square-integrable function, and is therefore associated with the probability density of a quantum-mechanical system. This function is expressible as a linear combination of the eigenstates of any 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 that observable to be the eigenvalue of the final state.
The quantum state of a physical system is described by a wave function (in turn—an element of a projective Hilbert space). This can be expressed as a vector using Dirac or bra–ket notation :
The kets specify the different quantum "alternatives" available—a particular quantum state.
Official source
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