Inverse problem for the Schrödinger equation with non-self-adjoint matrix potential

S. A. Avdonin, A. S. Mikhaylov, V. S. Mikhaylov, J. C. Park

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the dynamical system with boundary control for the vector Schrödinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the inverse problem of recovering the matrix potential from the dynamical Neumann-to-Dirichlet operator. We first provide a method to recover spectral data for the Schrödinger system and consequently prove controllability of the system. We then develop a strategy for solving the inverse problem using this method with other techniques of the boundary control method.

Original languageEnglish
Article number035002
Number of pages19
JournalInverse Problems
Volume37
Issue number3
Early online date31 Dec 2020
DOIs
StatePublished - Mar 2021

Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Applied Mathematics
  • Computer Science Applications
  • Mathematical Physics

Keywords

  • Boundary control method
  • Controllability
  • Inverse problem
  • Matrix potential
  • Schrödinger equation
  • Schr&#246
  • inverse problem
  • boundary control method
  • controllability
  • matrix potential
  • dinger equation

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