The _Heisenberg Equation of motion_ (Heisenberg EOM) is a dynamical equation equivalent to the [[Schrödinger Equation]] that models time evolution in terms of operators in the [Heisenberg picture](Heisenberg%20picture). These two operators are an arbitrarily [[observable]] $\hat{A}_H$ in the Heisenberg picture associated with a particular quantum system and its [Hamiltonian operator](Hamiltonian%20operator.md) $\hat{H}.$ The Heisenberg equation of motion is given as follows in terms of a [commutation relation](Commutators%20in%20quantum%20mechanics.md#Commuting%20and%20non-commuting%20pairs%20of%20observables) containing a [Hamiltonian,](Hamiltonian%20operator.md) $\hat{H}$ and an [observable,](Observable.md) $\hat{A}_H.$ $\frac{\partial}{\partial t}\hat{A}_H=\frac{i}{\hbar}[\hat{H},\hat{A}_H]$ # Correspondence with Poisson brackets [Poisson bracket](Poisson%20bracket.md) # Proof of Equivalence to the Schrödinger equation #QuantumMechanics/QuantumDynamics