Definitions for "Hamiltonian"
In classical mechanics, the sum of kinetic and potential energy functions (i.e., the total energy); in quantum mechanics, the corresponding linear Hermitian operator.
a mathematical operator that, when applied to such things as "wave functions," describes the total energy of a physical system
The operator H (consisting of potential and kinetic energy terms) which describes which operations are to be carried out on the wavefunction in the Schrödinger equation H. ("an operator is a symbol that tells you to do something to whatever follows the symbol" McQuarrie, 1983)
chain or circuit in a graph is said to be hamiltonian if each vertex of the graph appears in it precisely once. Paths and cycles of digraphs are called hamiltonian if the same condition holds. A graph containing a hamiltonian circuit, or a digraph containing a hamiltonian cycle is referred to as a hamiltonian graph or digraph.
cycle, path or curcuit In a graph a Hamiltonian path is a path that contains each vertex once and only once. A Hamiltonian cycle is a cycle that includes each vertex. [ Dossey, p. 108
(n.) A closed path through a graph which passes through each node in the graph exactly once.