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Relating to or invented by the mathematician Sir W. R. Hamilton, especially denoting concepts employed in the wave-mechanical description of particles.
- ‘The game is related to Euler's Knight's Tour problem since, in today's terminology, it asks for a Hamiltonian circuit in a certain graph.’
- ‘He realised the analogy with Poisson brackets in Hamiltonian mechanics.’
- ‘In mathematics he worked on the calculus of variations, Fourier series, function spaces, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity.’
- ‘In 1834, Dublin mathematician William Rowan Hamilton applied his work on characteristic functions in optics to Newtonian mechanics, and what is now called the Hamiltonian formalism of mechanics was born.’
- ‘A generalized version of the Pigeonhole is naturally used to show that the Petersen graph does not have Hamiltonian circuits.’
2Relating to the American statesman Alexander Hamilton or his doctrines.
- ‘The great statesmen of the first half of the 19th century, free traders to a man, were devoted to stopping the Hamiltonian power policy of executive power, entangling alliances and war, taxes and protectionism to benefit northern elites.’
- ‘During the boom years of the 1960s, a period of soaring idealism about ‘the people’ generally, an almost Hamiltonian contempt for the public held sway on Wall Street.’
- ‘More expansive still was the attitude towards Hamilton, again almost wholly in the North, that emerged from the carnage of the Civil War and the perception that Hamiltonian centralization would have prevented the war.’
- ‘US foreign policy during the 1990s was dominated by a conflict between Hamiltonian urges to build a global commercial order and Wilsonian desires to promote democracy and the protection of human rights.’
- ‘In turn, it should also be noted that both the Walpolean and the Hamiltonian views are remarkably similar to the view that lies behind France's or East Asia's postwar industrial policy.’
A Hamiltonian operator or function.
- ‘For a massive particle in zero gravity moving in one dimension, the Hamiltonian is just the kinetic energy, which in terms of momentum, not velocity, is just.’
- ‘Consider a system with a Hamiltonian which posses a quantum phase transition.’
- ‘Recently, Gonzalez and Maddocks performed a detailed theoretical analysis of the problem from the microscopic point of view where the probability measure is an exponential function of the Hamiltonian.’
- ‘The interaction Hamiltonian is then diagonalized and the resulting stick spectrum is dressed with Gaussians to simulate homogeneous broadening.’
- ‘In particular if you try to use the mapping in this manner, you will end up creating qubit Hamiltonians with very nonlocal interactions.’
2A follower or adherent of Alexander Hamilton or his doctrines.
- ‘On the one hand there are the Hamiltonians who place a great deal of trust in the executive branch to execute policy in a good faith manner.’
- ‘I say this not to argue against ‘judicial review’ - I'm a Hamiltonian - but to question whether the ‘even one participant’ assertion is valid.’
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