Some analytic efforts for the quantum effects near the singularity of Thomas-Fermi equation
سال انتشار: 1396
نوع سند: مقاله کنفرانسی
زبان: انگلیسی
مشاهده: 393
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شناسه ملی سند علمی:
ARSE01_070
تاریخ نمایه سازی: 22 دی 1396
چکیده مقاله:
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
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نویسندگان
Atefeh Hasan-Zadeh
Assistant Professor of Applied Mathematics, Fouman Faculty of Engineering, College of Engineering, University of Tehran, Iran
Hooman Fatoorehchi
Assistant Professor of Chemical Engineering, Tehran Faculty of Engineering, School of Chemical Engineering, College of Engineering, University of Tehran, Iran