Hamiltonian

American  

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

adjective

1. pertaining to or advocating Hamiltonianism.

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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

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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).

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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

Hamilton's approach became known as "Hamiltonian mechanics," and it proved extremely powerful.

From Science Daily • Mar. 10, 2026

Today, many quantum equations are still written in terms of total energy, referred to as the "Hamiltonian," derived from Hamilton's expression describing the energy of a mechanical system.

From Science Daily • Mar. 10, 2026

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

From Slate • Aug. 7, 2024

Take, for example, the fungal experiments of Selin Balci, one of five former Hamiltonian Artists fellows who return to the gallery in “Empirical Evidence.”

From Washington Post • Sep. 29, 2021

The Hamiltonian story required a distortion in the sequence of the exchange in order to preserve Hamilton’s posthumous reputation.

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