A New Class of Schrödinger Operators without Positive Eigenvalues

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.

References in corpus (3)

• Sub-exponential decay of eigenfunctions for some discrete Schrödinger operators
• Limiting Absorption Principle for Schrödinger Operators with Oscillating Potential
• On the limiting absorption principle for a new class of schroedinger hamiltonians