# Quantum Systems at The Brink

@inproceedings{Hundertmark2022QuantumSA, title={Quantum Systems at The Brink}, author={Dirk Hundertmark and Michal Jex and Markus Lange}, year={2022} }

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.

## One Citation

### Ju l 2 02 1 Quantum Systems at The Brink Existence and Decay Rates of Bound States at Thresholds ; Critical Potentials and dimensionality

- Mathematics
- 2021

One of the crucial properties of a quantum system is the existence of bound states. In this paper we present a necessary and sufficient condition for the Schrödinger operator to have a zero energy…

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