Application of Variational Method to the Thomas-Fermi Equation

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概要

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• Variational method is applied to derive two inequalities giving rigorous upper and lower bounds for the initial slope B_0 = -ψ'(0) of the ordinary Thomas-Fermi function ψ(x), the solution of the non-linear equation ψ'' = x^<-1/2> ψ<3/2> with the boundary conditions ψ(0) = 1, ψ(∞) = 0. Application of these formulas using simple trial functions leads to the estimate 1.5865 ≦ B_0 ≦ 1.5883.

• 社団法人日本物理学会の論文
• 1957-02-05

著者

• Ikebe Teruo

  Department Of Mathematics Faculty Of Science Kyoto University

• Ikebe Teruo

  Department Of Physics Faculty Of Science University Of Tokyo

• KATO Tosio

  Department of Physics, Faculty of Science, University of Tokyo

• Kato Tosio

  Department Of Mathematics University Of California

関連論文

• Completeness of Modified Wave Operators for Long-Range Potentials
• A Spectral Theory for the Reduced Wave Equation with a Complex Refractive Index
• Application of Variational Method to the Thomas-Fermi Equation
• Some Mathematical Problems in Quantum Mechanics
• Non-Existence of Bound States with Positive Energy
• Note on Schwinger's Variational Method
• On the Convergence of the Perturbation Method. I.
• Spectral Representation for Schrodinger Operators with Long-Range Potentials, II-Perturbation by Short-Range Potentials-
• On a Theorem for Estimating Eigenvalues
• Remarks on non-elliptic stationary wave propagation problems

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