# 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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