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

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 multipl...

Full description

Saved in:
Bibliographic Details
Published inAtoms Vol. 8; no. 3; p. 53
Main Author Straton, Jack C.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2020
Subjects
analytical
antihydrogen
antihydrogen ion
hydrogen ion
Integrals
Mathematical analysis
photodetachment
Plane waves
Polynomials
Quantum theory
radiative attachment
Transformations (mathematics)
Wave functions
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2218-2004
2218-2004
DOI:10.3390/atoms8030053