KetVektor

KetVektor is a term used in quantum mechanics and linear algebra to denote a ket vector, the state vector of a quantum system in Dirac notation. In German-language texts, KetVektor is commonly used to refer to the ket state |psi>, whereas English-language texts usually speak of 'ket vector' or simply '|psi>'.

A ket |psi> is an element of a complex Hilbert space H. When a basis {|i>} is chosen, |psi> can be written as |psi> = sum_i c_i |i>, with complex amplitudes c_i. The dual bra <phi| corresponds to the conjugate transpose of the ket, and the inner product is <phi|psi>. The norm is <psi|psi> and normalization is enforced by setting <psi|psi>=1 for a pure state.

Operations on ket vectors include the outer product |psi><phi|, which yields an operator on H, and the action of linear operators A: H -> H, giving A|psi>. The density operator for a pure state is rho = |psi><psi|; mixed states are represented by statistical ensembles of kets.

Common examples in a two-dimensional Hilbert space (a qubit) include the basis states |0> and |1>, and superpositions such as |+> = (|0>+|1>)/√2. Measurements produce outcomes with probabilities given by |<phi|psi>|^2, and expectation values of an observable A are <psi|A|psi>.

KetVektor is foundational in quantum mechanics and quantum information, linking state representation to observables, unitary evolution, and measurement. Historically, the concept arises from Paul Dirac's bra-ket notation introduced in the 1930s; in German texts the term KetVektor reflects the direct translation of 'ket vector.' See also Dirac notation, Hilbert space, bra, ket.