Quantum Hamiltonian 

In standard quantum mechanics, systems evolve according to the Schrödinger equation , where is a Hermitian matrix called the Hamiltonian. The following are possible Hamiltonians.

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The following matrices cannot be quantum Hamiltonians because they are not Hermitian.

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The matrix exponential is called the time-evolution operator and is always a unitary matrix (assuming the time and Planck's constant are real).

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