Dispersion for Schr\"odinger Operators with One-gap Periodic Potentials on R^1

Kaihua Cai

Dispersion for Schr\"odinger Operators with One-gap Periodic Potentials on R^1

Mathematical Physics 2007-05-23 v1 math.MP

Authors: Kaihua Cai

Abstract

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

Keywords

Schrödinger operators periodic potentials dispersion decay stationary phase

Cite

@article{arxiv.math-ph/0411002,
  title  = {Dispersion for Schr\"odinger Operators with One-gap Periodic Potentials on R^1},
  author = {Kaihua Cai},
  journal= {arXiv preprint arXiv:math-ph/0411002},
  year   = {2007}
}

Comments

23 pages

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