Hamilton, William Rowan

Hamilton, William Rowan 130n Hankel, Hermann 114n Heaviside, Oliver 63n Heisenberg, Werner 146n Helmholtz, Hermann von 38n Hermite, Charies L02n Hooke, Robert 90n Httckei, Erich 316n... 

Newton s formulation is not the only way in which classical equations of motion can be formulated. Lagrange (Joseph Louis Lagrange, France, 1736-1813), Hamilton (William Rowan Hamilton, Ireland, 1805-1865), and others developed different means, and it is the formulation of Hamilton that has proven the most useful framework for developing the mechanics of quantum systems. It is important to realize that Newtonian, Lagrangian, and Hamiltonian mechanics offer equivalent descriptions of classical systems. 

Gibbs also wrote an influential book on statistical mechanics, which developed a molecular theory of thermodynamic properties from first principles, with a treatment that was general enough to accommodate quantum mechanics, a theory that had not even been imagined yet. He championed the now standard use of vector notation over William Rowan Hamilton s quaternion algebra and wrote several seminal papers on electromagnetism in the 1880s that supported Maxwell s theory, see also Equilibrium Maxwell, James Clerk Thermodynamics. 

Hamiltonian mechanics refers to a mathematical formalism in classical mechanics invented by the Irish mathematician William Rowan Hamilton (1805-1865) during the early 1830 s arising from Lagrangian mechanics which was introduced about 50 years earlier by Joseph-Louis Lagrange (1736-1813). The Hamiltonian equations can however be formulated on the basis of a variational principle without recourse to Lagrangian mechanics [95] [2j. 

William Rowan Hamilton (1856). Memorandum respending a new system of Roots of Unity. Philosophical Magazine 12, 4, 446. 

The operator in the brackets in equation (1,14) is known as the Hamiltonian operator, since it is related to an expression for energy given by the Irish mathematician Sir William Rowan Hamilton (1805- 1865) this operator is given the symbol H ... 

Sir William Rowan Hamilton (1805-1865) devised an alternative form of Newton s equations of motion involving a function H, the Hamiltonian function for the system. For a system where the potential energy is a function of the coordinates only, the total energy remains constant with time that is, E is conserved. We shall restrict ourselves to such conservative systems. For conservative systems, the classical-mechanical Hamiltonian function turns out to be simply the total energy expressed in terms of coordinates and conjugate momenta. For Cartesian coordinates x, y, z, the conjugate momenta are the components of linear momentum in the x, y, and z directions p, Py, and p. ... 

William Rowan Hamilton (1805-1865) was an Astronomer Royal in Ireland. At the age of 17, he found an error in the famous Celestial Mechanks by Laplaoe. This drew the attention of scientists and was the beginning of Hamilton s scientific career. In this book, his name is repeated many times (because of the word Hamiltonian). At the age of 13 he knew about the same number of languages, among others Persian, Sanskrit, Arabic and Hindustani. 

In simple cases this is the sirni of its kinetic and potential energies. In Hamiltonian equations, the usual equations used in mechanics (based on forces) are replaced by equations expressed in terms of momenta. This method of formulating mechanics (Hamiltonian mechanics) was first introduced by Sir William Rowan Hamilton. 

William Rowan Hamilton (1805-1865) Irish physicist, astronomer, and mathematician Dublin, Ireland. 

FIGURE 9.3 Sir William Rowan Hamilton (1805-1865). Hamilton reformulated the law of motion of Newton and Lagrange into a form that ultimately provided a mathematical basis for modern quantum mechanics. He also invented matrix algebra. 

Storage, though, is all very well, but how can the information be written and retrieved An exploratory experiment, based, to be sure, on laborious biochemistry, was performed by L. M. Adleman more than a decade ago. As a first demonstration of the watery DNA computer in action he chose to solve a simple form of what mathematicians know as the Hamiltonian path, or travelling salesman problem—how, starting from city A, to travel to each of a succession of other cities, terminating at city Z, without ever retracing your path. A formal solution to this ancient mathematical teaser was worked out in the early nineteenth century by two mathematicians. Sir William Rowan Hamilton in Ireland and Thomas Kirkman in England. With their aid an answer can be easily found if the number of cities is small, but if there are many it requires an enormous amount of computer time. 

Hamilton (Sir) William Rowan (1805— 1865) Irish mathematician, introducer of quaterions, alternative formalism for tensor and vector calculation, widely used operation by Hamiltonian ... 

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