On the First Trace Formula for Schr\"odinger Operators

TL;DR

This paper proves that the first trace formula applies to all one-dimensional Schrödinger operators with real-valued integrable potentials, establishing a fundamental spectral relation.

Contribution

It extends the validity of the first trace formula to all Schrödinger operators on the line with integrable potentials, broadening previous results.

Findings

First trace formula holds for all Schrödinger operators with integrable potentials

Establishes a fundamental spectral relation for these operators

Provides a rigorous proof for the formula's universality in this setting

Abstract

We prove that the so-called first trace formula holds for all Schr\"odinger operators on the line with real-valued integrable potentials.