• Journal of the Korean Physical Society
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• v.73 no.11
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• pp.1612-1618
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• 2018

In this work, the ground-state properties of an interacting electron gas confined in a two-dimensional quantum dot system with the Gaussian potential ${\upsilon}(r)=V_0(1-{\exp}(-r^2/p))$, where $V_0$ and p are confinement parameters, are determined numerically by using the Thomas-Fermi approximation. The shape of the potential is modified by changing the $V_0$ and the p values, and the influence of the confining potential on the system's properties, such as the chemical energy, the density profile, the kinetic energy, the confining energy, etc., is analyzed for both the non-interacting and the interacting cases. The results are compared with those calculated for a harmonic potential, and excellent agreement is obtained in the limit of high p values for both the non-interacting and the interacting cases.

• Nuclear Engineering and Technology
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• v.10 no.3
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• pp.127-136
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• 1978

We have applied the temperature dependent Thomas-Fermi theory to evaluate the equations of state, chemical potentials, entropies, % ionizations, total energies and kinetic energies of an atom, and seveal thermodynamic quantifies of one of metallic substance, Na, for a density range of 0.1$\rho$$_{0}$ ~ 10$\rho$$_{0}$, where $\rho$$_{0}$ is the normal density of Na at its melting point, and for a temperature range of 60.88Ryd. ~0.0216 Ryd., where the system is expected to be in a gaseous or liquid state. The main interest of present work lies in physical quantities at high temperatures and high densities, however, we have included those quantities of Na at sufficiently low temperatures and low densities to show that the approximation is not so crude as one might expect. Particularly, at high temperatures, the calculated equations of state, kinetic energies of an atom, chemical potentials and entropies are compared with those, of an ideal Fermi gas. The results show that, at high temperatures, the agreement seems good for chemical Potentials. However, the differences in, entropy, kinetic energy of an atom, and equation of state are not negligible even at such high temperature as $textsc{k}$T=60.88Ryd.