Spectral Isoperimetric Inequality for the δ′-Interaction on a Contour

Abstract

We consider the problem of geometric optimization for the lowest eigenvalue of the two-dimensional Schrödinger operator with an attractive δ′-interaction of a fixed strength, the support of which is a C2-smooth contour. Under the constraint of a fixed length of the contour, we prove that the lowest eigenvalue is maximized by the circle. The proof relies on the min-max principle and the method of parallel coordinates.