论文标题
将一类二维积分降低到一维，并应用于高斯变换
Reducing a class of two-dimensional integrals to one-dimension with application to Gaussian Transforms
论文作者
论文摘要
量子理论在多维积分中浮现，这些积分包含集成变量，它们的倒数和这些变量的逆多项式中的指数。本文引入了一种将这种积分对减少到一个维度的手段，当集成剂包含幂的次数xy/（x+y）的任意函数乘以指数的各种组合。在某些情况下，这些指数直接来自涉及平面波，氢波函数，Yukawa和/或库仑电位的过渡分化。在其他情况下，这些指数源于此类功能的高斯变换。
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.
