Tight-binding approximation for semi-infinite solids. Application of a transform method and of delta function normalization

A transform method for treating semi‐infinite solids in the tight‐binding (TB) approximation is introduced. The difference equations for the TB orbital coefficients are converted, thereby, to convenient algebraic equations. For this purpose, a Dirac delta function normalization for the wave function is also introduced, instead of the usual box one. Single and coupled bands are treated, and the methods are applied elsewhere to electron transfer problems at interfaces.