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math-ph2025
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…
math-ph2016
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…
math-ph2015★ 8 cited
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…