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.


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.