A Remark on the Dirichlet–Neumann Decoupling and the Integrated Density of States

We prove an estimate on the difference of the number of eigenvalues for Schrِdinger operators with Dirichlet and Neumann boundary conditions in large boxes. In the proof, we use Kreinʹs theory of the spectral shift function. As an application, we show that the integrated density of states is independent of the choice of boundary conditions.