The Morse and Maslov indices for Schrödinger operators

@article{Latushkin2018TheMA,
  title={The Morse and Maslov indices for Schr{\"o}dinger operators},
  author={Yuri Latushkin and Selim Sukhtaiev and Alim Sukhtayev},
  journal={Journal d'Analyse Math{\'e}matique},
  year={2018},
  volume={135},
  pages={345-387}
}
We study the spectrum of Schrödinger operators with matrixvalued potentials, utilizing tools from infinite-dimensional symplectic geometry. Using the spaces of abstract boundary values, we derive relations between the Morse and Maslov indices for a family of operators on a Hilbert space obtained by perturbing a given self-adjoint operator by a smooth family of bounded self-adjoint operators. The abstract results are applied to the Schrödinger operators with θ-periodic, Dirichlet, and Neumann… 
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