Hamiltonian

American  

[ham-uhl-toh-nee-uhn] / ˌhæm əlˈtoʊ ni ən /

adjective

1. pertaining to or advocating Hamiltonianism.

---

noun

1. a supporter of Alexander Hamilton or Hamiltonianism.

Hamiltonian British  

/ ˌhæməlˈtəʊnɪən /

noun

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

---

adjective

1. denoting or relating to Sir William Rowan Hamilton, or to the theory of mechanics or mathematical operator devised by him

Hamiltonian Scientific  

/ hăm′əl-tō′nē-ən /

1. 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).

---

Etymology

Origin of Hamiltonian

An Americanism dating back to 1790–1800; Hamilton + -ian

Compare meaning

How does hamiltonian compare to similar and commonly confused words? Explore the most common comparisons:

• Hamiltonian vs. Jeffersonian

Example Sentences

See Examples For:

Hamiltonian

Looking ahead, the researchers plan to experimentally demonstrate Hamiltonian based measurement processes for quantum feedback control using superconducting qubits.

From Science Daily ● Jul. 3, 2026

Industrialization posed the question, the author writes, of whether, as the historian James Truslow Adams put it, “a Jeffersonian democracy could survive in a Hamiltonian economy.”

From The Wall Street Journal ● May 22, 2026

Morris was a Hamiltonian before Hamilton, a champion of a strong Congress and a strong president.

From Slate ● Aug. 7, 2024

Pieces by seven former Hamiltonian Artworks fellows are scattered through galleries filled primarily with items from the permanent collection — and even installed in a fireplace, which is where Amy Boone-McCreesh’s “Good Luck Charms” hangs.

From Washington Post ● Dec. 2, 2022

The flaw in such reasoning, however, would have been obvious to any accountant or investment banker with a modicum of Hamiltonian wisdom.

From "Founding Brothers: The Revolutionary Generation" by Joseph J. Ellis