Quantum Systems at The Brink

Abstract

We present a method to calculate the asymptotic behavior of eigenfunctions of Schrödinger operators that also works at the threshold of the essential spectrum. It can be viewed as a higher order correction to the well-known WKB method which does need a safety distance to the essential spectrum. We illustrate its usefulness on examples of quantum particles in a potential well with a long-range repulsive term outside the well.

arXiv admin note: substantial text overlap with arXiv:2012.12748

References in corpus (3)

• Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms
• Rigorous conditions for the existence of bound states at the threshold in the two-particle case
• Quantum Systems at the Brink: Existence of Bound States, Critical Potentials and Dimensionality