Planar Two-particle Coulomb Interaction: Classical and Quantum Aspects

TL;DR

This paper explores classical and quantum planar Coulomb interactions, using action-angle variables and harmonic oscillator approximations, comparing 2+1D results with the traditional 3+1D analysis.

Contribution

It introduces a detailed analysis of planar Coulomb interactions in both classical and quantum regimes, highlighting relativistic corrections and perturbation effects specific to 2+1 dimensions.

Findings

Relativistic corrections handled via action-angle variables.

Logarithmic potential complications discussed.

Comparison between 2+1D and 3+1D Coulomb interactions.

Abstract

The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent perturbation theory. Complications arising due to the logarithmic nature of the potential are pointed out. In the quantum case, harmonic oscillator approximations are considered and effects of the perturbations on the excited (oscillator) states have been analysed. In both the above cases, the known 3+1-dimensional analysis is carried through side by side, for a comparison with the 2+1-dimensional (planar) results.