Reducing a class of two-dimensional integrals to one-dimension with application to Gaussian Transforms

• URL: http://arxiv.org/abs/2005.07015v1
• Date: Sat, 9 May 2020 23:40:43 GMT
• Title: Reducing a class of two-dimensional integrals to one-dimension with application to Gaussian Transforms
• Authors: Jack C. Straton
• Abstract summary: This 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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