Dimensionally hybrid Green's functions and density of states for interfaces

The energy dependent Green's function (E-H)-1 for an interface Hamiltonian which interpolates between two and three dimensions can be calculated explicitly. This yields an expression for the density of states ϱ(E) in the system which interpolates continuously between the two-dimensional ϱ(E)=constant behavior for high energies and the three-dimensional ϱ(E)∝E behavior for low energies. The relation between electron density and Fermi energy in the system also interpolates between the two-dimensional and three-dimensional equations.