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Phase recovery from phaseless scattering data for discrete Schrödinger operators

Roman Novikov, Basant Lal Sharma

Abstract

We consider scattering for the discrete Schrödinger operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$, with compactly supported potential. We give formulas for finding the phased scattering amplitude from phaseless near-field scattering data.

Phase recovery from phaseless scattering data for discrete Schrödinger operators

Abstract

We consider scattering for the discrete Schrödinger operator on the square lattice , , with compactly supported potential. We give formulas for finding the phased scattering amplitude from phaseless near-field scattering data.
Paper Structure (5 sections, 3 theorems, 47 equations)

This paper contains 5 sections, 3 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Main Results
  3. Proofs of Theorem \ref{['thm2p1']} and formulas (\ref{['Dexp']}) and (\ref{['measE']})
  4. Proof of Proposition \ref{['prop2p4n']}
  5. Proofs of Propositions \ref{['prop2p4']} and \ref{['prop2p5']}

Key Result

Proposition 2.2

Suppose that the assumptions of Theorem thm2p1 for $d=2$ hold, and Then where $f^+_0=f^+_0(k, \omega)$.

Theorems & Definitions (13)

  • Remark 1.1
  • Remark 1.2
  • Proposition 2.2
  • Remark 2.3
  • Remark 2.4
  • Remark 2.5
  • Proposition 2.6
  • Proposition 2.7
  • Remark 2.8
  • Remark 2.9
  • ...and 3 more