## 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...