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Inverse Problem for the Schrödinger Equation in Dimension 3

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  • Fagueye Ndiaye
  • Dimitri Mugnai

Abstract

In this paper, we consider the Schrödinger equation in the unit ball in ℠3. We study the inverse problem of identifying the potential q from the Dirichlet to Neumann map which associates to all possible functions f on the boundary ∂B and the measurements of the normal derivative of the solution of Schrödinger equation ∂u/∂ν on ∂B. Using spherical harmonics tools, we determine an explicit expression for the potential qx on the edge of the domain from an explicit formula for the Dirichlet to Neumann map in a unit ball in dimension 3. We theoretically and numerically present an example.

Suggested Citation

  • Fagueye Ndiaye & Dimitri Mugnai, 2022. "Inverse Problem for the Schrödinger Equation in Dimension 3," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, February.
    • Handle: RePEc:hin:jjmath:2935392
    DOI: 10.1155/2022/2935392
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