Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Phase retrieval for solutions of the Schr{ö}dinger equations

Philippe Jaming

Abstract

In this note we present several questions about the phase retrieval problem for the Schr{ö}dinger equation. Some partial answers are given as well as some of the heuristics behind these questions.

Phase retrieval for solutions of the Schr{ö}dinger equations

Abstract

In this note we present several questions about the phase retrieval problem for the Schr{ö}dinger equation. Some partial answers are given as well as some of the heuristics behind these questions.

Paper Structure

This paper contains 3 sections, 3 theorems, 23 equations.

Table of Contents

  1. Introduction
  2. The Schrödinger equation on ${\mathbb{R}}^d$
  3. Schrödinger equations on finite graphs

Key Result

Proposition 1.1

Let $u_0,v_0\in L^2({\mathbb{R}}^d)$ and let $u,v$ be the solution of the free Schrödinger equation If $|u(t,x)|=|v(t,x)|$ for every $t\in{\mathbb{R}}$ and every $x\in{\mathbb{R}}^d$ then there exists $c\in{\mathbb{R}}$ such that $u_0=cv_0$.

Theorems & Definitions (8)

  • Proposition 1.1: Jaming Ja
  • Conjecture 2.1
  • Lemma 3.1
  • proof
  • Definition 3.2
  • Definition 3.3
  • Theorem 3.4
  • proof