Conversely, by rotating the basis for the state vector at each time by e, the time dependence in the matrices can be undone. The matrices are now time independent, but the state vector rotates, | ψ ψ ( t ) ⟩ ⟩ = e − − i H t | ψ ψ ( 0 ) ⟩ ⟩ , d | ψ ψ ⟩ ⟩ d t = − − i H | ψ ψ ⟩ ⟩ . This is the Schrödinger equation for the state vector, and this time-dependent change of basis amounts to transformation to the Schrödinger picture, with ⟨ x | ψ ⟩ = ψ (x).