Related papers: The two-dimensional hydrogen atom in The momentum …
We generalize Schroedinger's factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach, is the fact that the Hamiltonian is represented…
Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an `action' describing the motion of a…
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…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
The density of states and other thermodynamic functions of helium nanodroplets are calculated for a microcanonical ensemble with both energy and total angular momentum treated as conserved quantum numbers. These functions allow angular…
For the associated Legendre and Ferrers functions of the first and second kind, we obtain new multi-derivative and multi-integral representation formulas. The multi-integral representation formulas that we derive for these functions…
We leverage the power of neural quantum states to describe the ground state wave function of solid and liquid atomic hydrogen, including both electronic and protonic degrees of freedom. For static protons, the resulting Born-Oppenheimer…
The Schr\"odinger-Coulomb Sturmian problem in $\mathbb{R}^{N}$, $N\geqslant2$, is considered in the momentum representation. An integral formula for the Gegenbauer polynomials, found recently by Cohl [arXiv:1105.2735], is used to separate…
The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon…
This paper is focused on showing that the fully differential cross section of ionization during a collision of a proton and an antiproton with a hydrogen atom is directly expressed by the wave function in the coordinate representation. Wave…
The hierarchy of equations for reduced density matrices that describes a thermodynamically equilibrium quantum system obtained earlier by the author is investigated in the momentum representation. In the paper it is shown that the use of…
A light-front Hamiltonian reproducing the results of two-dimensional quantum electrodynamics in the Lorentz coordinates is constructed using the bosonization procedure and an analysis of the bosonic perturbation theory in all orders in the…
The term describing the coupling between total angular momentum and energy-momentum in the hydrogen atom is isolated from the radial Dirac equation and used to replace the corresponding orbital angular momentum coupling term in the radial…
The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the Levi-Civita…
The Lagrange-mesh method is a very accurate procedure to compute eigenvalues and eigenfunctions of a two-body quantum equation. The method requires only the evaluation of the potential at some mesh points in the configuration space. It is…
We formulate the equations for point vortex dynamics on a closed two dimensional Riemann manifold in the language of affine and other kinds of connections. The speed of a vortex is then expressed in terms of the difference between an affine…
This paper seeks to construct a representation of the algebra of angular momentum (SU(2) algebra) in terms of the operator relations corresponding to Gentile statistics in which one quantum state can be occupied by $n$ particles. First, we…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into…
The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions…