# The number of eigenvalues of the matrix Schr\"odinger operator on the half line with general boundary conditions

## TL;DR

This paper establishes a bound on the number of eigenvalues for matrix Schrödinger operators on the half line, considering general boundary conditions and integrable potentials with finite first moments.

## Contribution

It extends eigenvalue bounds to matrix Schrödinger operators with the most general self-adjoint boundary conditions at the origin.

## Key findings

- Derived a Bargmann-Birman-Schwinger type bound
- Applicable to operators with general boundary conditions
- Handles matrix potentials with finite first moments

## Abstract

We prove a bound, of Bargmann- Birman-Schwinger type, on the number of eigenvalues of the matrix Schr\"odinger operator on the half line, with the most general self adjoint boundary condition at the origin, and with selfadjoint matrix potentials that are integrable and have a finite first moment.