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Sep 24, 2013 at 15:48 comment added Zurab Silagadze My goal was to calculate $I_n$ in a different way (without using the known Landau-Zener formula) than discussed in the paper. I hope some method exists to get the asymptotic behaviour of $z(s)$ from the integral equation quoted (or from the equivalent differential equation). Then this will give $I_n$ and therefore another derivation of the Landau-Zener formula, which was the final goal.
Sep 24, 2013 at 13:58 history edited Jon CC BY-SA 3.0
Rephrasing
Sep 24, 2013 at 13:53 history answered Jon CC BY-SA 3.0