Abstract
There exists a remarkable connection between the quantum mechanical Landau-Zener problem and purely classical-mechanical problem of a ball rolling on a Cornu spiral. This correspondence allows us to calculate a complicated multiple integral, a kind of multi-dimensional generalization of Fresnel integrals. A direct method of calculation is also considered but found to be successful only in some low-dimensional cases. As a byproduct of this direct method, an interesting new integral representation for ζ(2) is obtained.
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Kholodenko, A.L., Silagadze, Z.K. When physics helps mathematics: Calculation of the sophisticated multiple integral. Phys. Part. Nuclei 43, 882–888 (2012). https://doi.org/10.1134/S1063779612060068
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DOI: https://doi.org/10.1134/S1063779612060068