Dispersion for Schrödinger Operators with One-gap Periodic Potentials on R^1

Abstract

We prove $t^{-\frac{1}{4}}-$decay for the solutions of the 1-dim Schrodinger equation with a one-gap periodic potential as $t\to +\infty$. Generically, one has $t^{-\frac{1}{3}}$-decay and this decay is optimal. Our approach is to analyze the stationary phase in the Schrödinger evolution as an integral operator.

23 pages

Cited by in corpus (1)

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