• Look up Hamiltonian in Wiktionary, the free dictionary. Hamiltonian may refer to: Hamiltonian mechanics, a function that represents the total energy of...
    1 KB (207 words) - 13:25, 12 October 2024
  • Thumbnail for Hamiltonian path
    theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or...
    18 KB (2,030 words) - 19:28, 20 September 2024
  • Thumbnail for Hamiltonian mechanics
    physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics...
    52 KB (9,277 words) - 18:05, 23 October 2024
  • In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential...
    27 KB (4,903 words) - 04:26, 29 August 2024
  • The Hamiltonian constraint arises from any theory that admits a Hamiltonian formulation and is reparametrisation-invariant. The Hamiltonian constraint...
    20 KB (3,745 words) - 20:35, 7 August 2023
  • molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei...
    38 KB (5,204 words) - 02:55, 8 July 2024
  • The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G...
    21 KB (2,518 words) - 19:02, 20 August 2024
  • A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system...
    10 KB (1,369 words) - 14:52, 1 April 2024
  • Hamiltonian simulation (also referred to as quantum simulation) is a problem in quantum information science that attempts to find the computational complexity...
    9 KB (1,181 words) - 14:01, 22 August 2024
  • physics, most commonly within condensed-matter physics, a gapped Hamiltonian is a Hamiltonian for an infinitely large many-body system where there is a finite...
    2 KB (259 words) - 12:25, 5 December 2022
  • In mathematics, a Hamiltonian matrix is a 2n-by-2n matrix A such that JA is symmetric, where J is the skew-symmetric matrix J = [ 0 n I n − I n 0 n ]...
    6 KB (651 words) - 00:44, 28 January 2023
  • interaction picture is a special case of unitary transformation applied to the Hamiltonian and state vectors. Operators and state vectors in the interaction picture...
    16 KB (2,285 words) - 01:30, 30 August 2024
  • The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of...
    22 KB (3,975 words) - 08:46, 9 August 2024
  • Hamiltonian complexity or quantum Hamiltonian complexity is a topic which deals with problems in quantum complexity theory and condensed matter physics...
    3 KB (385 words) - 21:40, 18 January 2024
  • Thumbnail for Hamiltonian Monte Carlo
    The Hamiltonian Monte Carlo algorithm (originally known as hybrid Monte Carlo) is a Markov chain Monte Carlo method for obtaining a sequence of random...
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  • Thumbnail for Hamiltonian decomposition
    mathematics, a Hamiltonian decomposition of a given graph is a partition of the edges of the graph into Hamiltonian cycles. Hamiltonian decompositions...
    13 KB (1,522 words) - 04:24, 19 August 2024
  • non-abelian Dedekind group is called a Hamiltonian group. The most familiar (and smallest) example of a Hamiltonian group is the quaternion group of order...
    4 KB (399 words) - 04:50, 16 September 2024
  • In theoretical physics, Hamiltonian field theory is the field-theoretic analogue to classical Hamiltonian mechanics. It is a formalism in classical field...
    12 KB (1,836 words) - 17:15, 16 April 2024
  • Hamiltonian truncation is a numerical method used to study quantum field theories (QFTs) in d ≥ 2 {\displaystyle d\geq 2} spacetime dimensions. Hamiltonian...
    22 KB (3,716 words) - 05:38, 31 March 2023
  • physics, a first-class constraint is a dynamical quantity in a constrained Hamiltonian system whose Poisson bracket with all the other constraints vanishes...
    27 KB (4,556 words) - 23:44, 7 September 2024
  • mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics. It asserts that the phase-space distribution function is constant...
    24 KB (3,887 words) - 18:56, 7 July 2024
  • corresponding Hamiltonian is called the Bose–Fermi–Hubbard Hamiltonian. The physics of this model is given by the Bose–Hubbard Hamiltonian: H = − t ∑ ⟨...
    27 KB (3,830 words) - 19:03, 28 June 2024
  • Thumbnail for Quaternion
    In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...
    96 KB (12,688 words) - 12:38, 27 October 2024
  • 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...
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  • Liouville's theorem in Hamiltonian mechanics follows. Symplectomorphisms that arise from Hamiltonian vector fields are known as Hamiltonian symplectomorphisms...
    9 KB (1,104 words) - 17:24, 15 August 2024
  • Hamiltonian optics and Lagrangian optics are two formulations of geometrical optics which share much of the mathematical formalism with Hamiltonian mechanics...
    34 KB (6,584 words) - 18:04, 23 October 2024
  • Hamiltonian coloring, named after William Rowan Hamilton, is a type of graph coloring. Hamiltonian coloring uses a concept called detour distance between...
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  • and corresponding generalized velocities in configuration space) and Hamiltonian mechanics (using coordinates and corresponding momenta in phase space)...
    40 KB (5,758 words) - 22:46, 21 September 2024
  • Thumbnail for Petersen graph
    The Petersen graph has a Hamiltonian path but no Hamiltonian cycle. It is the smallest bridgeless cubic graph with no Hamiltonian cycle. It is hypohamiltonian...
    24 KB (2,943 words) - 11:37, 25 October 2024
  • Nambu mechanics (category Hamiltonian mechanics)
    of Hamiltonian mechanics involving multiple Hamiltonians. Recall that Hamiltonian mechanics is based upon the flows generated by a smooth Hamiltonian over...
    6 KB (735 words) - 04:26, 12 February 2024