Taylor-Laplace Expansions of the Yukawa and Related Potential Energy Functions

摘要

In this paper we apply that form of the Taylor series to the Yukawa potential, and to several potential functions which can be derived from it. In particular, we examine the expansion of the Yukawa potential itself. In the limit as the exponent a vanishes, the Yukawa potential transforms into the Coulomb potential. We show that the limiting process applied to the Taylor series for the Yukawa potential yields the familiar form of the Laplace expansion of the Coulomb potential. Differentiation of the Yukawa potential with respect to the exponent a yields the exponential function. Hence, we develop a Taylor-Laplace power series representation of the Morse potential.