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Hamiltonian definition

hăməl-tōnē-ən
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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Of or characteristic of Alexander Hamilton or his federalist principles.
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A follower of Alexander Hamilton.
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Alternative capitalization of Hamiltonian.
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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.
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Other Word Forms

Noun

Singular:
hamiltonian
Plural:
hamiltonians

Origin of hamiltonian

  • After Sir William Rowan Hamilton (1805–1865), Irish mathematician

    From American Heritage Dictionary of the English Language, 5th Edition

Hamiltonian Sentence Examples

  • Among his principal publications are An Examination of Ferrier's "Knowing and Being," and the Scottish Philosophy - (a work which gave him the reputation of being an independent Hamiltonian in philosophy); Memoir of John Brown, D.D.

  • If the system is supposed to obey the conservation of energy and to move solely under its own internal forces, the changes in the co-ordinates and momenta can be found from the Hamiltonian equations aE aE qr = 49 - 1 57., gr where q r denotes dg r ldt, &c., and E is the total energy expressed as a function of pi, qi,.

  • To this reaction Hamilton explicitly appealed in the convention of 1787; and of this reaction various features of the constitution, and Hamiltonian federalism generally, were direct fruits.

  • It is, however, unquestionably true, that as a startling protest against measures" to silence,"in Jefferson's words," by force and not by reason the complaints or criticisms, just or unjust, of our citizens against the conduct of our agents,"they served, in this respect, a useful purpose; and as a counterblast against Hamiltonian principles of centralization they were probably, at that moment, very salutary; while even as pieces of constitutional interpretation it is to be remembered that they did not contemplate nullification by any single state, and, moreover, are not to be judged by constitutional principles established later by courts and war.

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