vågfunktionen

Vågfunktionen is the state description used in quantum mechanics to describe a quantum system. In the standard non-relativistic formulation, the state of a single particle is represented by a complex-valued function ψ(x,t) called the wave function. The quantity |ψ(x,t)|^2 gives the probability density for finding the particle at position x at time t, according to the Born rule. The wave function is normalized so that ∫|ψ(x,t)|^2 dx = 1.

The time evolution of the wave function is governed by the Schrödinger equation: iħ ∂ψ/∂t = Hψ, where H is the Hamiltonian operator of the system. For a time-independent Hamiltonian, solutions can be expressed as stationary states ψ_n(x) with energies E_n, and general states are linear superpositions of these eigenfunctions.

In the position representation, ψ(x,t) contains all accessible information about a pure state; in the momentum representation, the wave function is obtained by a Fourier transform of ψ(x,t). The wave function is defined up to a global phase, which has no observable consequences.

For systems with more than one particle, the wave function depends on the coordinates of all particles and must be (anti)symmetrized under particle exchange to account for indistinguishable bosons or fermions. Measurements of observables correspond to operators, and the probability of obtaining a given eigenvalue is given by the squared magnitude of the projection of the state onto the corresponding eigenstate.

Different interpretations of quantum mechanics offer varied views on the meaning of the wave function. In the Copenhagen view, wave function collapse is a postulate during measurement; other approaches attribute collapse to processes like decoherence or reinterpret the wave function as a state of knowledge.