Abstract
For finite systems of a sphere, a disc, and a linear line, the smoothed electron density of states (DOS) is derived directly from the distribution of eigenvalues on one-particle model. The DOS for a sphere is expressed as the sum of three terms: volume, surface, and circumference. The change in the DOS from a microsystem to a macrosystem is clarified. Comparison with the results by Balian and Bloch is carried out and it is shown that the present results give better agreement with the exact DOS. The effect of boundary condition on the DOS is investigated.
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