Hamiltonian Quick reference
The Concise Oxford Dictionary of Mathematics (6 ed.)
...Hamiltonian See Hamiltonian mechanics...
Hamiltonian Quick reference
A Dictionary of Chemistry (8 ed.)
... (Symbol H ) . A function used to express the energy of a system in terms of its momentum and positional coordinates. In simple cases this is the sum 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 ( 1805–65 ) in 1834–35 . The Hamiltonian operator is used in quantum mechanics in the Schrödinger equation...
Hamiltonian Quick reference
A Dictionary of Physics (8 ed.)
...Hamiltonian Symbol H . A function used to express the energy of a system in terms of its momentum and positional coordinates. In simple cases this is the sum 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. These concepts, often called Hamiltonian mechanics , were formulated by Sir William Rowan Hamilton ( 1805–65...
spin hamiltonian Reference library
Oxford Dictionary of Biochemistry and Molecular Biology (2 ed.)
...hamiltonian a formulation in quantum mechanics used in the determination of the energy levels of the spin of an electron or a nucleus in electron spin resonance spectroscopy or, less commonly, in nuclear magnetic resonance spectroscopy . See also Hamiltonian operator...
Hamiltonian cycle Quick reference
A Dictionary of Computer Science (7 ed.)
... cycle ( Hamilton cycle ) A cycle of a graph in the course of which each vertex of the graph is visited once and once...
Hamiltonian graph Quick reference
The Concise Oxford Dictionary of Mathematics (6 ed.)
...Hamiltonian graph In graph theory, one area of study concerns the possibility of travelling around a graph , going along edges in such a way as to visit every vertex exactly once. A Hamiltonian cycle is a cycle that contains every vertex, and a graph is called Hamiltonian if it has a Hamiltonian cycle. The term arises from Hamilton’s interest in the existence of such cycles in the graph formed from the dodecahedron ’s vertices and edges. Compare eulerian graph...
Hamiltonian mechanics Quick reference
The Concise Oxford Dictionary of Mathematics (6 ed.)
...Hamiltonian mechanics A rewriting of Lagrange’s equations which foreshadowed advances in statistical mechanics and quantum theory . In the notation of Lagrange’s equations, we set p i = ∂ L / ∂ q ˙ i and introduce the Hamiltonian H ( q , p , t ) = ∑ i = 1 n p i q i − L ( q , p , t ) . Hamilton’s equations then have the form d q i d t = ∂ H ∂ p i , d p i d t = − ∂ H ∂ q i ....
Hamiltonian operator Reference library
Oxford Dictionary of Biochemistry and Molecular Biology (2 ed.)
... operator symbol : H ; a function used to express the total energy of a system in joules: H = T + V , where T is the kinetic energy operator and V the potential energy operator. For a particle of mass m and momentum p , H = p 2 / 2 m + V . [After William Rowan Hamilton ( 1805–65 ), Irish astronomer and...
Lagrange–Hamiltonian mechanics Quick reference
A Dictionary of Mechanical Engineering (2 ed.)
...Lagrange–Hamiltonian mechanics Newtonian mechanics expressed in terms of energy rather than forces. Particularly useful for determining the trajectories of objects moving in a gravitational...
Hamiltonian Reference library
The Oxford Dictionary of New Zealandisms
... • noun a person born or resident in Hamilton. • adjective of or relating to Hamilton or Hamiltonians...
Hamiltonian Reference library
The New Oxford Dictionary for Scientific Writers and Editors (2 ed.)
... Symbol: H A function used in general dynamics: H = ∑ i p i q • i − L , where p i are the *generalized momenta , q i are the *generalized coordinates , and L is the *Lagrangian function . Also called Hamiltonian function...
Hamiltonian
spin hamiltonian
Hamiltonian cycle
counting problem
Goldstone's theorem
Noether's theorem
