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arXiv · 2005.07015

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

Jack C. Straton
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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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Jack C. Straton. 2020-05-09. Reducing a class of two-dimensional integrals to one-dimension with application to Gaussian Transforms. https://doi.org/10.3390/atoms8030053

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