Hamiltonian may refer to

In both mathematics and physics (specifically mathematical physics), (after William Rowan Hamilton):

the term Hamiltonian refers to any energy function defined by a Hamiltonian vector field, a particular vector field on a symplectic manifold;

more specifically, as an adjective it is used in the phrases:

In mathematical physics (after William Rowan Hamilton):

  • Hamiltonian system
  • Hamiltonian flow
  • Hamiltonian vector field
  • Hamiltonian mechanics in classical mechanics
  • Hamilton's principle
  • Hamilton–Jacobi equation

In mathematics (after William Rowan Hamilton):

  • Hamiltonian path, in graph theory
    • Hamiltonian cycle, a special case of a Hamiltonian path
  • Hamiltonian group, in group theory
  • Hamiltonian matrix
  • Hamiltonian numbers (or quaternions)

In physics (after William Rowan Hamilton):

  • Hamiltonian (quantum mechanics)
  • Molecular Hamiltonian
  • Hamiltonian constraint
  • Hamiltonian fluid mechanics
  • Hamiltonian lattice gauge theory

In Chemistry

  • Molecular Hamiltonian
  • Dyall Hamiltonian

In control theory (after William Rowan Hamilton):

  • Hamiltonian (control theory)
  • Hamilton–Jacobi–Bellman equation

In Language (after educationist James Hamilton (1769–1831) (de-wiki))

  • Hamiltonian method

Other uses:

  • Hamiltonian economic program as put forward by the eighteenth century American politician Alexander Hamilton
  • a demonym for a person from any of several places named Hamilton.