8 citations · 12 across the 7 of their papers we have counts for
7 papers
Some exact solutions of the Schrödinger--Poisson system in spaces of constant sectional curvature
Richard Chapling
We consider the Schrödinger--Poisson system on the complete, simply-connected Riemannian manifolds of constant sectional curvature. We obtain closed-form stationary spherically-sym…
Symmetric Potentials Beget Symmetric Ground States
Richard Chapling
Using an unusual type of symmetric average, we show that for several common equations involving quite general potentials possessing symmetry, the ground state, if it exists, must a…
Invariant Meromorphic Functions on the Wallpaper Groups
Richard Chapling
We construct the meromorphic functions invariant under the action of the sense-preserving wallpaper groups on the complex plane. We discuss possible generalisa-tions of this to the…
Note on Closed-Form Expressions for Irreducible Loop Integrals
Richard Chapling
We provide a new analysis of the irreducible loop integrals first considered in a 2003 paper of Wu. Using convergence ideas from probability, we produce conditions on the regulator…
Bound States of the One-Dimensional Maxwell--Schrödinger Equations
Richard Chapling
We prove the existence of a ground state of the Maxwell--Schrödinger equations in one spatial dimension, describing a specified amount of free charge under the influence of a fixed…
Asymptotics of Certain Sums Required in Loop Regularisation
Richard Chapling
We consider the three conjectures stated in a 2003 paper of Wu, concerning the asymptotics of particular sums of products of binomials, powers and logarithms. These sums relate to…
A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
Richard Chapling
We consider Poisson's equation on the -dimensional sphere in the situation where the inhomogeneous term has zero integral. Using a number of classical and modern hypergeometric…