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  1. A Hamiltonian is a mathematical function that can be used systematically and with great generality to generate the equations of motion of a dynamic system. The Hamiltonian is equivalent in many cases to the sum of the kinetic energy and potential energy of a system expressed in terms of the system's coordinates and momenta treated as independent variables.

  2. It is also the mathematical operator that generates such a function.

The Hamiltonian is named after the Irish mathematician William Rowan Hamilton, who first formulated it.

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