The Jost solutions for general Gaussian potentials

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Abstract
The explicit Born series which represent the regular solutions (of the Schrödinger equation), the Jost solutions, and the Jost functions analytic in some domains of complex wave numbers and angular momenta are found for general potentials of the Gaussian type expressed by the Stiltjes integral. When finding their form we make use of the analogy with the corresponding solutions for general potentials of the Yukawa type, which is based on the special representations of the Bessel and Hankel functions (purely kinematic solutions) in either case. Some other relations are also derived.

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