Integration of a generalized Hénon–Heiles Hamiltonian

Integration of a generalized Hénon-Heiles Hamiltonian

The generalized Hénon-Heiles Hamiltonian H = 1/2(P 2 X + P 2 Y + c1X 2 + c2Y 2) + aXY 2 − bX3/3 with an additional nonpolynomial term μY −2 is known to be Liouville integrable for three sets of values of (b/a, c1, c2). It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in...

A Numerical Integration Method by Using Generalized Series of Functions

Generalized Quantum Search Hamiltonian

There are hamiltonians that solve a search problem of finding one of N items in O( √ N) steps. They are hamiltonians to describe an oscillation between two states. In this paper we propose a generalized search hamiltonian, Hg. Then the known search hamiltonians become special cases of Hg. From the generalized search hamiltonian, we present remarkable results that searching with 100% is subject ...

Hamiltonian properties of generalized pyramids

We investigate here the hamiltonicity and traceability of a class of polytopes generalizing pyramids, prisms, and polytopes with Halin 1-skeleta.

a numerical integration method by using generalized series of functions