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Time Evolution Equation

The time evolution equation, \frac{d|\Psi\rangle}{dt} = H|\Psi\rangle, describes how the wavefunction changes over time under the influence of the Hamiltonian operator.
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The statement of the theorem

Let H\mathcal{H} be a separable Hilbert space, and let ∣Ψ(t)⟩∈H|\Psi(t)\rangle \in \mathcal{H} be the state vector describing the system at time tt. Define the Hamiltonian operator H:H→HH: \mathcal{H} \to \mathcal{H} as the generator of time translations, such that HH is self-adjoint (H=H†H = H^{\dagger}). The time evolution of the state vector is governed by the differential equation:\nddt∣Ψ(t)⟩=−iℏH∣Ψ(t)⟩\frac{d}{dt}|\Psi(t)\rangle = -\frac{i}{\hbar} H |\Psi(t)\rangle
Source: Wikipedia