|1.||a mathematical function of the coordinates and momenta of a system of particles used to express their equations of motion|
|2.||H a mathematical operator that generates such a function|
|3.||denoting or relating to Sir William Rowan Hamilton, or to the theory of mechanics or mathematical operator devised by him|
|Hamiltonian (hām'əl-tō'nē-ən) Pronunciation Key
A mathematical function or operator that can be used to describe the state of a physical system. In classical mechanics, the Hamiltonian is a function of coordinates and momenta of bodies in the system, treated as independent variables. It is equal to the sum of the kinetic and potential energies of the system, and can be used to derive the equations of motion for the system. In quantum mechanics, the Hamiltonian is an operator corresponding to the total energy of the system. The Hamiltonian is named after Irish mathematician William Rowan Hamilton (1805-1865).