# Thomas-Fermi equation

## Thomas-Fermi equation

[′täm·əs ′fer·mē i‚kwā·zhən]
(atomic physics)
The differential equation x 1/2(d 2 y / dx 2)= y 3/2that arises in calculating the potential in the Thomas-Fermi atom model; the physically meaningful solution satisfies the boundary conditions y (0)=1 and y (∞)=0.
References in periodicals archive ?
Additionally, an adaptive algorithm for the Thomas-Fermi equation by means of the moving mesh finite element method has been developed [31].
An adaptive algorithm for the Thomas-Fermi equation. Numerical Algorithms, 59(3):359-372, 2012.
Also, it is tried that a history for Thomas-Fermi equation is provided.
In this paper, it is attempted to introduce a Spectral method based on the generalized fractional order of the Chebyshev functions for solving Thomas-Fermi equation.
The nonlinear singular Thomas-Fermi equation is defined as [24, 25, 26]:
Pirkhedri, "The sinc-collocation method for solving the Thomas-Fermi equation," Journal of Computational and Applied Mathematics, vol.
The corresponding homogeneous Thomas-Fermi equation is
Thomas-Fermi Equation in the Presence of Minimal Length
Now, the Thomas-Fermi equation ([[nabla].sup.2] - [[lambda].sup.2])U(r) = 0 in this case transforms to the following equation:
While the use of only real coefficients is less robust and cannot easily be applied to multimodal functions, it is still suitable for the Thomas-Fermi equation. On the other hand due to it simpler form it has some specific properties.
In this paper, a new approach for solving the Thomas-Fermi equation using spectral methods has been presented.
Adomian, "Solution of the Thomas-Fermi equation," Applied Mathematics Letters, vol.
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