Nonuniqueness of scattering amplitudes at special points

TL;DR

This paper reveals that in one-dimensional quantum scattering, amplitudes are not uniquely determined at specific parameter points, linking this to pole-skipping phenomena in holography and potential scattering problems.

Contribution

It identifies and analyzes the nonuniqueness of scattering amplitudes at special points, connecting quantum mechanics with holographic pole-skipping phenomena.

Findings

Scattering amplitudes are non-unique at special parameter points.

The nonuniqueness relates to potential scattering with angular momentum.

Connection established between quantum scattering and holographic pole-skipping.

Abstract

We point out little discussed phenomenon in elementary quantum mechanics. In one-dimensional potential scattering problems, the scattering amplitudes are not uniquely determined at special points in parameter space. We examine a few explicit examples. We also discuss the relation with the pole-skipping phenomena recently found in holographic duality. In the holographic pole-skipping, the retarded Green's functions are not uniquely determined at imaginary Matsubara frequencies. It turns out that this universality comes from the fact that the corresponding potential scattering problem has the angular momentum potential.