# On the over-barrier reflection in quantum mechanics with multiple degrees of freedom

## TL;DR

This paper presents an analytic two-dimensional quantum system demonstrating that over-barrier reflection probability varies non-monotonically with energy, showing minimal suppression at specific optimal energies where reflection probability is significantly enhanced.

## Contribution

It introduces an analytic example of a 2D quantum system with non-monotonic over-barrier reflection suppression, highlighting the existence of optimal energies for reflection.

## Key findings

- Reflection probability is non-monotonically dependent on energy.
- Minimal suppression occurs at specific optimal energies.
- Reflection probability can be exponentially larger at these energies.

## Abstract

We present an analytic example of two dimensional quantum mechanical system, where the exponential suppression of the probability of over-barrier reflection changes non-monotonically with energy. The suppression is minimal at certain "optimal" energies where reflection occurs with exponentially larger probability than at other energies.