Trace Identities for the matrix Schr\"odinger operator on the half line with general boundary conditions

TL;DR

This paper establishes trace identities for the matrix Schrödinger operator on the half line, accommodating general boundary conditions and selfadjoint matrix potentials, extending previous results to more general settings.

Contribution

It generalizes Buslaev-Faddeev trace identities to matrix Schrödinger operators with arbitrary boundary conditions and selfadjoint potentials on the half line.

Findings

Proved trace identities for the matrix Schrödinger operator.

Extended identities to operators with general boundary conditions.

Applicable to selfadjoint matrix potentials.

Abstract

We prove Buslaev-Faddeev trace identities for the matrix Schr\"odinger operator on the half line, with general boundary conditions at the origin, and with selfadjoint matrix potentials.