A New Class of Schrödinger Operators without Positive Eigenvalues

2017/11/20 by Martin, Alexandre
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1711.07381

Abstract

Following the proof given by Froese and Herbst in [FH82] with another conjugate operator, we show for a class of real potential that possible eigenfunction of the Schrödinger operator has to decay sub-exponentially. We also show that, for a certain class of potential, this bound can not be satisfied which implies the absence of strictly positive eigenvalues for the Schrödinger operator.

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