Kvanttitilaa
Kvanttitila (Finnish for quantum state) is a central concept in quantum mechanics. It encapsulates all information needed to predict the outcomes of measurements performed on a system and to describe its time evolution. In quantum theory, states come in two principal forms: pure states and mixed states. A pure state is represented by a unit vector |ψ⟩ in a Hilbert space, or equivalently by a wavefunction ψ(x). A mixed state represents a statistical ensemble of pure states and is described by a density operator ρ, with ρ = ∑i p_i |ψ_i⟩⟨ψ_i|.
Time evolution of a closed quantum system is unitary. For a pure state, |ψ(t)⟩ evolves according to
Observables are represented by operators, and expected values are ⟨A⟩ = Tr(Aρ). For composite systems, states can