Wave function collapse: Difference between revisions

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Upon performing measurement of an [[observable]] ''A'', the probability of collapsing to a particular eigenstate of ''A'' is [[directly proportional]] to the square modulus of the (generally [[complex number|complex]]) amplitude associated with it. Hence, in experiments such as the [[double-slit experiment]] each individual [[photon]] arrives at a discrete point on the screen, but as more and more photons are accumulated, they form an interference pattern overall. After the collapse, the system begins to evolve again according to the Schrödinger equation.

WhyThe thecluster wavefunctionof appearsphenomena todescribed by the expression ''wavefunction collapse'' is a (perhaps <i>the</i>) fundamental questionproblem in the interpretation of quantum mechanics. The questionproblem is sweptnot underreally the rugconfronted by the [[Copenhagen interpretation]] (which simply postulates that itthis is indeeda collapsedspecial bycharacteristic of the act of "measurement," whichprocess. unfortunately isn't well-defined) and theThe [[Everett many-worlds interpretation]] (which assertsdeals thatwith it by reformulating the apparentrelation collapsebetween ismeasurement merelyapparatus and system, in such a subjectiveway illusionthat resultingthe fromlinear laws of [[quantum decoherence]])mechanics are universally valid.

See also [[mathematical formulation of quantum mechanics]]; the collapse of the wavefunction is postulate (3).

Note that a general description of the evolution of quantum mechanical systems is possible by using [[density matrix|density operators]] and [[quantum operation]]s. In this formalism (which is closely related to the C*-algebraic formalism) the collapse of the wave function corresponds to a non-unitary quantum operation.