A new approach to the problem of existence
and uniqueness of the minimizer of Fermi
energy

Atefeh Hasan-Zadeh

doi:https://doi.org/10.14445/22315373/IJMTT-V53P551

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 6 | Year 2018 | Article Id. IJMTT-V53P551 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P551

A new approach to the problem of existence and uniqueness of the minimizer of Fermi energy

Atefeh Hasan-Zadeh

Citation :

Atefeh Hasan-Zadeh, "A new approach to the problem of existence and uniqueness of the minimizer of Fermi energy," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 6, pp. 420-423, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P551

Abstract

This paper deals with Thomas-Fermi equation which is formulated as an Euler-Lagrange equation associated with the Fermi energy functional. Drawing upon advanced ingredients of Sobolev spaces and weak solutions, an analytic methodology is presented for the quantum correction near the origin of Thomas-Fermi equation. By this approach the existence and uniqueness of the minimizer for the energy functional of the Thomas-Fermi equation has been proved. It has been demonstrated that by the definition of such a functional and the relevant Sobolev spaces, the Thomas-Fermi equation, particularly of a neutral atom, extends to the nonlinear Poisson equation. Accordingly, weak solutions for more general Euler-Lagrange equation with more singularities are proposed.

Keywords

Euler-Lagrange equation, Fermi energy, Thomas-Fermi equation, Weak solution.

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