Oct 18, 2010 · I'm looking for an explanation on how reducing the Hamiltonian cycle problem to the Hamiltonian path's one (to proof that also the latter is NP-complete). I couldn't find any on the web, …

There are $\frac {n-1} {2}$ such consecutive pairs in the upper half of the circumference with $\frac {n-1} {2}$ edges connecting them each leading to unique edge disjoint Hamiltonian circuits.

Aug 18, 2020 · Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once Hamiltonian cycle is a Hamiltonian path that is a cycle, and a cycle is closed trail in …

Dec 17, 2025 · The discussion centers on the eigenvalues of an unusual Hamiltonian for a harmonic oscillator, defined as , where the operator is not self-adjoint. The commutation relation leads to the …

Sep 1, 2017 · The energy operator and the Hamiltonian operator are distinct entities in quantum mechanics. The discussion clarifies that while both operators can act on wave functions, they …

Apr 29, 2016 · The Hamiltonian is not always equivalent to the total energy of a system in classical mechanics. While it is often identified with total energy, exceptions arise in specific scenarios, such …

A Hamiltonian circuit (or cycle) visits every vertex exactly once before returning to its starting point. An Eulerian circuit visits every edge exactly once in the graph before returning to the starting point.

Nov 16, 2017 · Hello, I am trying to "integrate into my understanding" the difference between Hamiltonian and Lagrangian mechanics. In a nutshell: If Lagrange did all the work and formulated L …

Dec 6, 2024 · The discussion clarifies the concepts of "on-shell" and "off-shell" in Hamiltonian mechanics, emphasizing their relevance in phase space trajectories. A trajectory is classified as on …

Jul 17, 2011 · The discussion focuses on the calculation of the commutators of the Hamiltonian with position and momentum operators in quantum mechanics. Specifically, the user encounters a factor …