Abstract
We present a simple cellular method for the exact solution of the single-particle Schr\odinger equation of a complex system. It uses basis functions which are locally exact solutions within each potential cell. The wave-function expansion coefficients are determined by the boundary conditions between the neighboring cells, which can be specified on spheres instead of the cell boundaries. The method can yield an exact first-principles tight-binding theory with only nearest-neighbor couplings. Tests of the method using the two-dimensional empty lattice and the hydrogen molecule ion indicate that it converges rapidly and yields accurate results.
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