The total energy of any physical system is given by its [Hamiltonian.](Hamiltonians.md) In quantum mechanics this energy expression comes about from the application of an [observable](Observable.md) called the _Hamiltonian operator._ ^658f3f # Quantizing a classical Hamiltonian # Time independent Hamiltonian operators [[Hamiltonian operator (time independent)]] # Time dependent Hamiltonian operators .md#^f68af8) #^0290d2) # Free particle ## Free particle in a Quantum Field ## particle under a potential The most general form of a Hamiltonian of a in a potential $V$ is expressed as $\hat{H}=\frac{\hat{p}^2}{2m}+V$ where $\hat{p}$ is the [Momentum Operator](Quantum%20Mechanics/Quantum%20Measurement/Momentum%20Operator.md) and setting $V=0$ returns the [Free particle](Hamiltonian%20operator.md#Free%20particle) Hamiltonian. ## particle under a potential in a Quantum Field #QuantumMechanics/QuantumMeasurement/QuantumObservables