The Maslov and Morse indices for Schrödinger operators on ℝ

2016/08/19 by Howard, Peter, Latushkin, Yuri, Sukhtayev, Alim
#34L15 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.05692

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 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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