Note on 2D Schr\"odinger operators with delta-interactions on angles and crossing lines

TL;DR

This paper improves spectral bounds for 2D Schrödinger operators with delta-interactions on angles and crossing lines, relevant for quantum three-body problems, by sharpening previous estimates using a unified method.

Contribution

It provides new lower bounds on the spectrum of 2D Schrödinger operators with delta-interactions supported on angles and crossing lines, extending previous results.

Findings

Sharper lower bounds on the spectrum for angles

Lower bounds for crossing lines operators

Application to three-body quantum problems

Abstract

In this note we sharpen the lower bound from [LLP10] on the spectrum of the 2D Schroedinger operator with a delta-interaction supported on a planar angle. Using the same method we obtain the lower bound on the spectrum of the 2D Schroedinger operator with a delta-interaction supported on crossing straight lines. The latter operators arise in the three-body quantum problem with delta-interactions between particles.