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Abstract
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Using the Schrodinger-Poisson system in this paper, the basic quantum features of plasmon excitations in a free noninteracting €
electron gas with arbitrary degeneracy are investigated. The standing wave solution of the free electron gas is derived from the
corresponding linearized pseudo-force system with appropriate boundary conditions. It is shown that the plasmon excitation
energies for electron gas confined in an infinite potential well are quantized eigenvalues of which are obtained. It is found that
any arbitrary degenerate quantum electron gas possesses two different characteristic length scales, unlike the classical dilute
electron gas, with the smaller length scale corresponding to the single particle oscillation and the larger one due to the collective
Langmuir excitations. The probability density of the free electron gas in a box contains fine structures which are modulated over
a larger pattern. The envelope probability density profile for the electron Fermi gas confined in an impenetrable well in different
energy states is found to be quite similar to that of the free electron confined to an infinite potential well. However, the illustrative features of the plasmon theory presented in this research can be further elaborated in order to illuminate a wide range of
interesting physical phenomena involving both the single particle and the collective features.
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