Dispersion for Schrödinger Operators with One-gap Periodic Potentials on R¹

2004/10/31 by Kaihua Cai, Cai, Kaihua
Mathematics · Physics and Astronomy · #35J10 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:35J10

paper · pdf · doi:10.48550/arxiv.math-ph/0411002

23 pages

arxiv created 2004/10/31 · arxiv updated 2009/12/01

Abstract

We prove t^{- \frac 14}-decay for the solutions of the 1-dim Schrodinger equation with a one-gap periodic potential as t → +∞ . Generically, one has t^{- \frac 13}-decay and this decay is optimal. Our approach is to analyze the stationary phase in the Schrödinger evolution as an integral operator.

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