Hamiltonian
Encyclopedia
Hamiltonian may refer to
In mathematics (after William Rowan Hamilton
):
In physics (after William Rowan Hamilton
):
In Chemistry
In Language
Other uses:
In mathematics (after William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
):
- Hamiltonian systemHamiltonian systemIn physics and classical mechanics, a Hamiltonian system is a physical system in which forces are momentum invariant. Hamiltonian systems are studied in Hamiltonian mechanics....
- Hamiltonian pathHamiltonian pathIn the mathematical field of graph theory, a Hamiltonian path is a path in an undirected graph that visits each vertex exactly once. A Hamiltonian cycle is a cycle in an undirected graph that visits each vertex exactly once and also returns to the starting vertex...
, in graph theory- Hamiltonian cycle, a special case of a Hamiltonian path
- Hamiltonian groupHamiltonian groupIn group theory, a Dedekind group is a group G such that every subgroup of G is normal.All abelian groups are Dedekind groups.A non-abelian Dedekind group is called a Hamiltonian group....
, in group theory - Hamiltonian (control theory)Hamiltonian (control theory)The Hamiltonian of optimal control theory was developed by L. S. Pontryagin as part of his minimum principle. It was inspired by, but is distinct from, the Hamiltonian of classical mechanics. Pontryagin proved that a necessary condition for solving the optimal control problem is that the control...
- Hamiltonian matrix
- Hamiltonian flow
- Hamiltonian vector fieldHamiltonian vector fieldIn mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field, defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is a geometric manifestation of Hamilton's equations...
- Hamiltonian numbers (or quaternions)
In physics (after William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
):
- Hamiltonian systemHamiltonian systemIn physics and classical mechanics, a Hamiltonian system is a physical system in which forces are momentum invariant. Hamiltonian systems are studied in Hamiltonian mechanics....
- Hamiltonian mechanicsHamiltonian mechanicsHamiltonian mechanics is a reformulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton.It arose from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, but can be formulated without...
in classical mechanics - Hamilton's principleHamilton's principleIn physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action...
- Hamilton–Jacobi equationHamilton–Jacobi equationIn mathematics, the Hamilton–Jacobi equation is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations. In physics, the Hamilton–Jacobi equation is a reformulation of classical mechanics and, thus, equivalent to other formulations such as...
- Hamilton–Jacobi–Bellman equation
- Hamiltonian (quantum mechanics)Hamiltonian (quantum mechanics)In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
- Molecular HamiltonianMolecular HamiltonianIn atomic, molecular, and optical physics as well as in quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the energy of the electrons and nuclei in a molecule...
- Hamiltonian constraintHamiltonian constraintIn loop quantum gravity, dynamics such as time-evolutions of fields are controlled by the Hamiltonian constraint. The identity of the Hamiltonian constraint is a major open question in quantum gravity, as is extracting of physical observables from any such specific constraint.The Thiemann operator...
- Hamiltonian fluid mechanicsHamiltonian fluid mechanicsHamiltonian fluid mechanics is the application of Hamiltonian methods to fluid mechanics. This formalism can only apply to nondissipative fluids.-Irrotational barotropic flow:Take the simple example of a barotropic, inviscid vorticity-free fluid....
- Hamiltonian lattice gauge theoryHamiltonian lattice gauge theoryIn physics, Hamiltonian lattice gauge theory is a calculational approach to gauge theory and a special case of lattice gauge theory in which the space is discretized but time is not...
- Hamiltonian vector fieldHamiltonian vector fieldIn mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field, defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is a geometric manifestation of Hamilton's equations...
In Chemistry
- Molecular HamiltonianMolecular HamiltonianIn atomic, molecular, and optical physics as well as in quantum chemistry, molecular Hamiltonian is the name given to the Hamiltonian representing the energy of the electrons and nuclei in a molecule...
- Dyall Hamiltonian
In Language
- Hamiltonian method
Other uses:
- Hamiltonian economic programHamiltonian economic programThe Hamiltonian economic program was the set of measures that were proposed by American Founding Father and 1st Secretary of the Treasury Alexander Hamilton in three notable reports and implemented by Congress during George Washington's first administration....
as put forward by the eighteenth century American politician Alexander HamiltonAlexander HamiltonAlexander Hamilton was a Founding Father, soldier, economist, political philosopher, one of America's first constitutional lawyers and the first United States Secretary of the Treasury... - a demonym for a person from any of several places named HamiltonHamilton- Australia :* Hamilton, New South Wales, suburb of Newcastle** Hamilton railway station, New South Wales* Hamilton, Queensland, suburb of Brisbane* Hamilton, South Australia* Hamilton, Tasmania* Hamilton, Victoria* Hamilton Island, Queensland- Canada :...
.