Related papers: On the Hylleraas Coordinates
We consider energies defined as the Dirichlet integral of curves taking values in fast-oscillating manifolds converging to a linear subspace. We model such manifolds as subsets of $R^{m+m'}$ described by a constraint…
Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and…
Lame equation arises from deriving Laplace equation in ellipsoidal coordinates; in other words, it's called ellipsoidal harmonic equation. Lame function is applicable to diverse areas such as boundary value problems in ellipsoidal geometry,…
We present some formulae for the moments of inertia of homogeneous solids of revolution in terms of the functions that generate the solids. The development of these expressions exploits the cylindrical symmetry of these objects, and avoids…
In a molecule subjected to no external fields, motion of nuclei is governed by a function V of nuclear coordinates. This function (potential energy) is a sum of two terms: Coulomb repulsion between nuclei and the electronic effective…
We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…
The hybrid form is a combination of the Rydberg potential and the London inverse-sixth-power energy. It is accurate at all relevant distance scales and simple enough for use in all-atom simulations of biomolecules. One may compute the…
The interactions between atoms and molecules may be described by a potential energy function of the nuclear coordinates. Non-bonded interactions are dominated by repulsive forces at short range and attractive dispersion forces at long…
A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to…
We consider the recovery of a potential associated with a semi-linear wave equation on $\mathbb{R}^{n+1}$, $n\geq 1$. We show a H\"older stability estimate for the recovery of an unknown potential $a$ of the wave equation $\square u +a…
Similar to the Schwarzschild coordinates for spherical black holes, the Baldwin, Jeffery and Rosen (BJR) coordinates for plane gravitational waves are often singular, and extensions beyond such singularities are necessary, before studying…
The Configuration Interaction (CI) method using a large Laguerre basis restricted to l = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that…
An analysis of one and two point functions of the energy momentum tensor on homogeneous spaces of constant curvature is undertaken. The possibility of proving a $c$-theorem in this framework is discussed, in particular in relation to the…
The Schr\"odinger equation in phase space is used to calculate the Wigner function for the Helium atom in the approximation of a system of two oscillators. Dissipation effect is analysed and the non-classicality of the state is studied by…
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar $\phi$ with…
A one-electron Schroedinger equation based on special one-electron potentials for atoms is shown to exist that produces orbitals for an arbitrary molecule that are sufficiently accurate to be used without modification to construct single-…
We classify integrable Hamiltonian equations in 3D with the Hamiltonian operator d/dx, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w such that w_x=u_y. Based on the method…
We extend the recently derived factorization formula for energy-energy correlators to study the analytic structure of general $\nu$-point projected energy correlators in heavy ion collisions. The $\nu$-point projected energy correlators…
The hydrogen atom is supposed to be described by a generalization of Schr\"{o}dinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-\beta}$. Starting from previously obtained solutions…
Consider a finite dimensional complex Hilbert space $\cH$, with $dim(\cH) \geq 3$, define $\bS(\cH):= \{x\in \cH \:|\: ||x||=1\}$, and let $\nu_\cH$ be the unique regular Borel positive measure invariant under the action of the unitary…