A New Class of Schr\"odinger Operators without Positive Eigenvalues

Alexandre Martin

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arXiv · 1711.07381

A New Class of Schr\"odinger Operators without Positive Eigenvalues

Alexandre Martin

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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 Schr\"odinger 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 Schr\"odinger operator.

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BibTeX RIS

Alexandre Martin. 2017-11-20. A New Class of Schr\"odinger Operators without Positive Eigenvalues. https://arxiv.org/abs/1711.07381

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