Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Authors

Jack C. Straton, Portland State UniversityFollow

Published In

Atoms

Document Type

Article

Publication Date

9-2020

Subjects

Particles (Nuclear physics), Radiative capture, Photoionization, Hydrogen ions, Positrons, Antiprotons

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 multiplied by 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, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

Rights

Copyright 2020 by the author. Licensee MDPI, Basel, Switzerland.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Locate the Document

https://doi.org/10.3390/atoms8030053

DOI

10.3390/atoms8030053

Persistent Identifier

https://archives.pdx.edu/ds/psu/33691

Citation Details

Straton, J.C. Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms. Atoms 2020, 8, 53.