Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map Academic Article uri icon

abstract

  • 2019, Springer Nature B.V. It has been recently shown that the nodal deficiency of an eigenfunction is encoded in the spectrum of the Dirichlet-to-Neumann operators for the eigenfunctions positive and negative nodal domains. While originally derived using symplectic methods, this result can also be understood through the spectral flow for a family of boundary conditions imposed on the nodal set, or, equivalently, a family of operators with delta function potentials supported on the nodal set. In this paper, we explicitly describe this flow for a Schrdinger operator with separable potential on a rectangular domain and determine a mechanism by which lower-energy eigenfunctions do or do not contribute to the nodal deficiency.

published proceedings

  • Letters in Mathematical Physics

altmetric score

  • 1.25

author list (cited authors)

  • Berkolaiko, G., Cox, G., & Marzuola, J. L.

citation count

  • 3

complete list of authors

  • Berkolaiko, Gregory||Cox, Graham||Marzuola, Jeremy L

publication date

  • July 2019