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

Abstract

Assuming a symmetric potential that approaches constant endstates with a sufficient asymptotic rate, we relate the Maslov and Morse indices for Schrödinger 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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