Stability of the classical catenoid and Darboux-P\"oschl-Teller potentials

Abstract

We revisit the stability (instability) of the outer (inner) catenoid connecting two concentric circular rings and give an explicit new construction of the unstable mode of the inner catenoid by studying the spectrum of an exactly solvable one-dimensional Schr\"odinger operator with an asymmetric Darboux-P\"oschl-Teller potential.