When physics helps mathematics: calculation of the sophisticated multiple integral

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 $\zeta (2)$ is obtained.

13 pages, no figures

References in corpus (1)

• Matrix exponential solution of the Landau-Zener problem

Cited by in corpus (4)

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