Tilstandsvektorens

Tilstandsvektorens is the possessive form used in Norwegian to refer to the state vector, a fundamental concept in both physics and engineering. The state vector is a compact mathematical object that encodes all information necessary to describe the current condition of a dynamical system and to predict its future evolution under a given model.

In quantum mechanics, the state vector, commonly denoted |ψ>, belongs to a Hilbert space and provides probabilities for measurement outcomes through amplitudes. Its time evolution is described by the Schrödinger equation iħ ∂|ψ>/∂t = H|ψ>, where H is the system's Hamiltonian. For a pure state, the state vector contains all information about the system; mixed states require a density operator.

In classical and quantum control and signal processing, the state vector x(t) collects the state variables of a system, such as position and velocity, or other essential quantities. For a linear time-invariant model, the dynamics are written as dx/dt = A x + B u, with outputs y = C x + D u; the vector x has dimension n and its initial value x(0) determines the evolution.

State estimation uses the concept to reconstruct the state from measurements, via observers or Kalman filters in noisy environments. The tilstandsvektorens thus serves as a unifying framework to describe, simulate, and infer the behavior of complex systems across disciplines.