Reducing a class of two-dimensional integrals to one-dimension with application to Gaussian Transforms
General Mathematics
2020-09-29 v1 Quantum Physics
Abstract
Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers times an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.
Cite
@article{arxiv.2005.07015,
title = {Reducing a class of two-dimensional integrals to one-dimension with application to Gaussian Transforms},
author = {Jack C. Straton},
journal= {arXiv preprint arXiv:2005.07015},
year = {2020}
}