Integral representations for products of two solutions of the Airy equation with shifted arguments and their applications in physics

• URL: http://arxiv.org/abs/2311.12352v1
• Date: Tue, 21 Nov 2023 05:08:42 GMT
• Title: Integral representations for products of two solutions of the Airy equation with shifted arguments and their applications in physics
• Authors: K. V. Bazarov, O. I. Tolstikhin
• Abstract summary: This generalizes similar integral representations for the case $z_0$ obtained by Reid. Results are used to obtain the outgoing-wave Green's function for an electron in a static electric field in a closed analytic form.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Integral representations for a complete set of linearly independent products of two solutions of the Airy equation whose arguments differ by $z_0$ are obtained using the Laplace contour integral method. This generalizes similar integral representations for the case $z_0=0$ obtained by Reid. The relation to other previous results is discussed. The results are used to obtain the outgoing-wave Green's function for an electron in a static electric field in a closed analytic form.

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