Abstract
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.
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