Hamiltonianadj.n.
/hamɪlˈtəʊnɪən/ A. adj.
a. Pertaining to James Hamilton (1769–1831), or to his system of teaching languages.
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b. Pertaining to the Scottish philosopher and logician, Sir William Hamilton (1788–1856).
c. Pertaining to or invented by the Irish mathematician, Sir William Rowan Hamilton (1805–65), as Hamiltonian equation, Hamiltonian function, Hamiltonian operator.
d. Pertaining to or holding the doctrines of the American statesman, Alexander Hamilton, a leader of the Federalist party (1757–1804).
B. n.
A follower of any of the above.
ΚΠ
1826 S. Smith Wks. (1869) 531 We would have Hamiltonian keys to all these books.
1858 S. A. Allibone Crit. Dict. Eng. Lit. I. 755 Hamilton, James, ‘author of the Hamiltonian system’, excited much attention in the learned world by his publications..of interlinear English translations of books in various languages.
1864 F. C. Bowen Treat. Logic viii. 228 (heading) The Hamiltonian Doctrine of Syllogisms.
1864 F. C. Bowen Treat. Logic viii. 252 Under the Hamiltonian doctrine of eight fundamental Judgments, we have five hundred and twelve conceivable Moods.
1879 H. Adams Gallatin 174 Laying entirely aside the general proposition that the Hamiltonian Federalists considered a national debt as in itself a desirable institution.
Draft additions 1993
2. Mathematics. (See A. c). In classical mechanics, a function used to describe a system of particles in terms of a set of generalized coordinates, the Lagrangian of the system, and the associated generalized momenta, and which is equal to the total energy of the system if time is not mentioned explicitly in the expression. Also transferred, esp. of the Hamiltonian operator in Quantum Mechanics.
ΘΚΠ
the world > matter > physics > mechanics > dynamics > [noun] > specific function
H1835
Hamiltonian1926
Lagrangian1938
the world > matter > physics > quantum theory > quantum mechanics > [noun] > function or operator
Hamiltonian1926
1926 Proc. Royal Soc. A. 110 565 A dynamic system is determined on the classical theory by a Hamiltonian H, which is a certain function of the p's and q's, and the classical equations of motion may be written ẋ = [x, H].
1935 Physical Rev. 47 851/2 The energy is given by the equation E0 = ∫...ψHψdτ in terms of the Hamiltonian, H, and the normalized wave function ψ.
1961 J. L. Powell & B. Crasemann Quantum Mech. xi. 403 A system subject to a weak time-dependent perturbation can be described approximately by a Hamiltonian of the form H = H0 + V(t).
1978 P. W. Atkins Physical Chem. xiii. 419 This H plays a very special role in quantum mechanics, and is called the Hamiltonian or Hamiltonian operator for the system.
1981 A. D. Pierce Acoustics viii. 405 For the harmonic oscillator, the hamiltonian is p2/2m + ½kq2, where m is mass and k is spring constant.
This entry has not yet been fully updated (first published 1898; most recently modified version published online March 2022).
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adj.n.1826