"Potato kugel" for nuclear forces and a small one for acoustic waves

TL;DR

This paper extends the 'potato kugel' theorem, originally about harmonic functions, to the modified Helmholtz and Helmholtz equations, relevant for nuclear forces and acoustic waves, revealing new inverse properties.

Contribution

It introduces a novel extension of the 'potato kugel' theorem to equations modeling nuclear and acoustic phenomena, broadening its applicability.

Findings

Extended the theorem to modified Helmholtz and Helmholtz equations

Revealed inverse properties for nuclear forces and acoustic waves

Provided mathematical framework for new inverse problems

Abstract

The "potato kugel" theorem of Aharonov, Schiffer and Zalcman, which concerns an inverse property of harmonic functions, is extended to the settings of the modified Helmholtz and Helmholtz equations that describe nuclear forces and acoustic waves respectively.