| 释义 |
Hamiltonian, a. (n.)|hæmɪlˈtəʊnɪən|
[f. the surname Hamilton + -ian.]
A. adj.
a. Pertaining to James Hamilton (1769–1831), or to his system of teaching languages.
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.
1826Syd. Smith Wks. (1869) 531 We would have Hamiltonian keys to all these books. 1858Allibone 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. 1864Bowen Logic viii. 228 (heading) The Hamiltonian Doctrine of Syllogisms. Ibid. 252 Under the Hamiltonian doctrine of eight fundamental Judgments, we have five hundred and twelve conceivable Moods. 1879H. Adams Gallatin 174 (Cent.) Laying entirely aside the general proposition that the Hamiltonian Federalists considered a national debt as in itself a desirable institution.
Senses A. a–d in Dict. become A. 1–4. Add: [B.] 2. Math. [See A. 3.] 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 used transf., esp. of the Hamiltonian operator in Quantum Mech.
1926Proc. R. Soc. A. CX. 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] . 1935Physical Rev. XLVII. 851/2 The energy is given by the equation E0 = ∫...ψHψdτ in terms of the Hamiltonian, H, and the normalized wave function ψ. 1961[see perturbation n. 4]. 1978P. 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. 1981A. D. Pierce Acoustics viii. 405 For the harmonic oscillator, the hamiltonian is p2/2m + ½kq2 , where m is mass and k is spring constant. |