Corpus ID: 119700998

The Maslov and Morse indices for Schrödinger operators on $\mathbb{R}$

@article{Howard2016TheMA,
  title={The Maslov and Morse indices for Schr{\"o}dinger operators on \$\mathbb\{R\}\$},
  author={P. Howard and Y. Latushkin and A. Sukhtayev},
  journal={arXiv: Dynamical Systems},
  year={2016}
}
Assuming a symmetric potential that approaches constant endstates with a sufficient asymptotic rate, we relate the Maslov and Morse indices for Schr\"odinger operators on $\mathbb{R}$. In particular, we show that with our choice of convention, the Morse index is precisely the negative of the Maslov index. 

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