Wave function collapse1

In quantum mechanics, wave function collapse (also called collapse of the state vector orreduction of the wave packet) is the phenomenon in which a wave function—initially in a superpositionof several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer. In simplified terms, it is the reduction of the physical possibilities into a single possibility as seen by an observer. It is one of two processes by which quantum systems evolve in time, according to the laws of quantum mechanics as presented by John von Neumann.^[1] The reality of wave function collapse has always been debatable, i.e., whether it is a fundamental physical phenomenon in its own right or just an epiphenomenon of another process, such as quantum decoherence.^[2] In recent decades the quantum decoherence view has gained popularity.^{[citation needed]}Collapse may be understood as an update in a probabilistic model, given the observed result.

Mathematical terminology

For an explanation of the notation used, see Bra-ket notation.

The quantum state, or wave function, of a physical system at some point in time can be expressed in Dirac or bra-ket notation as:

where the s specify the different quantum "alternatives" available (technically, they form an orthonormal eigenvector basis, which implies ). An observable or measurable parameter of the system is associated with each eigenbasis, with each quantum alternative having a specific value or eigenvalue, e_i, of the observable.

The  are the probability amplitude coefficients, which are complex numbers. For simplicity we shall assume that our wave function is normalized, which means that