[ham-uh
l-toh-nee-uhn] 
| 1. | pertaining to or advocating Hamiltonianism. |
| 2. | a supporter of Alexander Hamilton or Hamiltonianism. |
| Hamilton, Alexander 1755?-1804. American politician. The first U.S. secretary of the treasury (1789-1795), he established the national bank and public credit system. Hamilton was mortally wounded in a duel with his political rival Aaron Burr. Ham'il·to'ni·an (-tō'nē-ən) adj. & n. |
| Ham·il·to·ni·an (hām'əl-tō'nē-ən) n. Abbr. H A mathematical function that can be used to generate the equations of motion of a dynamic system, equal for many such systems to the sum of the kinetic and potential energies of the system expressed in terms of the system's coordinates and momenta treated as independent variables. [After Sir William Rowan Hamilton (1805-1865), Irish mathematician.] |
| 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). |