English

Quantifying momenta through the Fourier transform

Analysis of PDEs 2016-08-14 v1 Classical Physics

Abstract

Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be calculated using only Fourier transforms. This result is used to evaluate the mean value of momenta associated to the symmetries of the reduced wave equation. As an explicit example, the orbital angular momenta of plane and elliptic-cylindrical waves is presented.

Keywords

Cite

@article{arxiv.1101.3121,
  title  = {Quantifying momenta through the Fourier transform},
  author = {B. M. Rodríguez-Lara},
  journal= {arXiv preprint arXiv:1101.3121},
  year   = {2016}
}

Comments

12 pages

R2 v1 2026-06-21T17:12:52.337Z