 For our purposes, the most important features of this equation is that it is deterministic and linear. The state vector at any time, together with the equation, uniquely determines the state vector at any other time. Linearity means that, if two vectors \(\ket{\psi_1(0)}\) and \(\ket{\psi_2(0)}\) evolve into vectors \(\ket{\psi_1(t) }\) and \(\ket{\psi_2(t)}\), respectively, then, if the state at time 0 is a linear combination of these two, the state at any time \(t\) will be the corresponding linear combination of \(\ket{\psi_1(t)}\) and \(\ket{\psi_2(t)}\).