discrete mathematics - What is the difference between a Hamiltonian ...
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 …
Reduction from Hamiltonian cycle to Hamiltonian path
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, …
Two equivalent statements of time reversal symmetric Hamiltonian ...
Dec 20, 2025 · SUMMARY The discussion centers on the equivalence of two conditions for time reversal invariant Hamiltonians: [H, Θ] = 0 and H = H ∗. Participants clarify that in Fourier space, the …
K5 Graph: Hamiltonian Circuits & Analysis • Physics Forums
Aug 6, 2013 · The existence of Hamiltonian circuits in K5 is confirmed by the fact that any complete graph with more than two vertices possesses at least one Hamiltonian cycle. Understanding of …
Is the Hamiltonian always the total energy? - Physics Forums
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 …
Hamiltonian Function - Definition & Explanation - Physics Forums
Sep 28, 2007 · The Hamiltonian function, denoted as H (p, q, t), is a fundamental concept in Hamiltonian mechanics that describes the energy of a system in terms of momentum (p), position (q), and time …
Energy operator and the Hamiltonian operator: Are they same?
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 …
Angular momentum commutes with Hamiltonian - Physics Forums
Oct 17, 2005 · The Hamiltonian operator commutes with the angular momentum operators (Lx, Ly, Lz) for systems such as the free particle, harmonic oscillator, and hydrogen atom, indicating a …
How many Hamiltonian cycles are there in a complete graph
Just bringing in all related similar numbers of Hamiltonian circuits in complete graphs with possible intuitive interpretation of them: Total (non-distinct) Hamiltonian circuits in complete graph Kn K n is (n …
Eigenvalues of a "unusual" Hamiltonian of a harmonic oscillator
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 …