Abstract
AbstractWe study finite‐size effects of the spatially bounded quantum systems exemplified by a single‐electron quantum dot with a harmonic potential and an impenetrable boundary. A general solution of the corresponding Schrödinger equation is obtained and the unique special solution for any energy is derived from the normalization and boundary conditions. The classical‐mechanically allowable eigenenergies form the continuous spectrum or piecewise continuous bands with the minimum value being much less than the zero point energy of a free harmonic oscillator. As the increase of the confining size, the band widths reduce and the energies finally close to the discrete level of the free oscillator. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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