The one-dimensional Coulomb oscillator

The One-dimensional Spinless Relativistic Coulomb Problem

Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a (“hard-core amended”) Coulomb interaction potential in one dimension. We prove the existence of a critical coupling constant (which contradicts the assertions of the previous analysis) and give analytic upper bounds on the energy eigenvalues....

On the classical two-dimensional one-component Coulomb plasma

Boundary Effects in the One Dimensional Coulomb Gas

We use the functional integral technique of Edwards and Lenard [1] to solve the statistical mechanics of a one dimensional Coulomb gas with boundary interactions leading to surface charging. The theory examined is a one dimensional model for a soap film. Finite size effects and the phenomenon of charge regulation are studied. We also discuss the pressure of disjunction for such a film. Even in ...

Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit.

An efficient way of evolving a solution to an ordinary differential equation is presented. A finite element method is used where we expand in a convenient local basis set of functions that enforce both function and first derivative continuity across the boundaries of each element. We also implement an adaptive step-size choice for each element that is based on a Taylor series expansion. This al...

Minimum energy state of the one-dimensional Coulomb chain

One-dimensional chains of laser-cooled ions have recently been confined in the fields of electromagnetic traps. This paper considers the minimum energy states of this one-dimensional ~1D! form of condensed matter. Molecular dynamics simulations of the minimum energy states are compared to a density functional theory of the inhomogeneous crystal. Unlike 2D and 3D inhomogeneous Coulombic systems,...