In elementary quantum mechanics, the state of a quantum-mechanical system is represented by a complex-valued wavefunction ψ (x, t). More abstractly, the state may be represented as a state vector, or ket, | ψ ⟩. This ket is an element of a Hilbert space, a vector space containing all possible states of the system. A quantum-mechanical operator is a function which takes a ket | ψ ⟩ and returns some other ket | ψ′ ⟩.