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

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.