# 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…

## 10 Citations

Counting spectrum via the Maslov index for one dimensional -periodic Schrödinger operators

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We study the spectrum of the Schrodinger operators with $n\times n$ matrix valued potentials on a finite interval subject to $\theta-$periodic boundary conditions. For two such operators,…

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- 2014

We study the Schr\"odinger operator $L=-\Delta+V$ on a star-shaped domain $\Omega$ in $\mathbb{R}^d$ with Lipschitz boundary $\partial\Omega$. The operator is equipped with quite general Dirichlet-…

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Working with general linear Hamiltonian systems on [0, 1], and with a wide range of self-adjoint boundary conditions, including both separated and coupled, we develop a general framework for relating…

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We show that the spectral flow of a one-parameter family of Schrödinger operators on a metric graph is equal to the Maslov index of a path of Lagrangian subspaces describing the vertex conditions. In…

Hadamard-type formulas via the Maslov form

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- 2016

Given a star-shaped bounded Lipschitz domain $${\Omega\subset{\mathbb{R}}^d}$$Ω⊂Rd, we consider the Schrödinger operator $${L_{\mathcal{G}}=-\Delta+V}$$LG=-Δ+V on $${\Omega}$$Ω and its restrictions…

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