Abstract
Approximate solutions to the Thomas–Fermi equation with so-called 'quantum correction terms' have been obtained by the use of a variational method. The results for krypton support the conclusions of Tomishima and Yonei that the coefficient of the gradient term should be 9/5 of the value derived by Kirzhnits. On the other hand, when the use of these equations is restricted to a region of the atom where the gradient expansion of Kirzhnits might be expected to be valid, the Kirzhnits value of the constant gives the better results, but the best results are obtained with no correction term at all (i.e. with the Thomas–Fermi–Dirac equation).
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