# Wave function collapse

 related topics {math, energy, light} {math, number, function} {theory, work, human}

In quantum mechanics, wave function collapse (also called collapse of the state vector or reduction of the wave packet) is the process by which a wave function—initially in a superposition of different eigenstates—appears to reduce to a single one of the states after interaction with an observer. In simplified terms, it is the condensation of physical possibilities into a single occurrence, 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 debated, 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 a change in conditional probabilities.

## Contents

### Mathematical terminology

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

where the $\scriptstyle |i \rang$s specify the different quantum "alternatives" available (technically, they form an orthonormal eigenvector basis, which implies $\scriptstyle \lang i | j \rang = \delta_{ij}$). An observable or measurable parameter of the system is associated with each eigenbasis, with each quantum alternative having a specific value or eigenvalue, ei, of the observable.

The $\scriptstyle \psi_i = \lang i|\psi \rang$ are the probability amplitude coefficients, which are complex numbers. For simplicity we shall assume that our wave function is normalised, which means that

With these definitions it is easy to describe the process of collapse: when an external agency measures the observable associated with the eigenbasis then the state of the wave function changes from $\scriptstyle |\psi\rang$ to just one of the $\scriptstyle |i\rang$s with Born probability $\scriptstyle | \psi_i | ^ 2$, that is: