Numerical determination of surface density of states in one-dimensional crystals

A discretization method is derived to investigate the continuous as well as the discrete part of the energy spectrum of the one-dimensional Schrödinger equation. The local density of states is made explicit and the example of a crystal surface is considered. It is shown that resonant states can be obtained if some extrinsic surface state (in a coated surface) falls in the range of an allowed energy band. An example is provided where extrinsic surface states interact with intrinsic (Tamm or Shockley) states. This phenomenon has a deep influence on the behavior of the energy levels of an adsorbed molecule during the adsorption process.