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Relation to the von Weizsäcker correction. In 1935, Carl Friedrich von Weizsäcker proposed the addition of an inhomogeneity term (sometimes referred to as a von Weizsäcker correction) to the kinetic energy of the Thomas–Fermi (TF) theory of atoms. The von Weizsäcker correction term is
The kinetic energy functional incorporates a TF term and the so-called von Weizsäcker correction [7,10, 13, 15,18,23]. This term captures the energy cost of rapid variation of the denisty in ...
It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker, [2] and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. The formula gives a good approximation for atomic masses and thereby other effects.
Publisher. The Physical Principles of the Quantum Theory (German: Physikalischen Prinzipien der Quantentheorie publisher: S. Hirzel Verlag, 1930) by Nobel laureate (1932) Werner Heisenberg and subsequently translated by Carl Eckart and Frank C. Hoyt. The book was first published in 1930 by University of Chicago Press.
This article is a summary of what is know rigorously about Thomas-Fermi (TF) theory with and without the Dirac and von Weizsäcker corrections. It is also shown that TF theory agrees asymptotically, in a certain sense, with nonrelativistic quantum theory as the nuclear charge z tends to infinity.
- Elliott H. Lieb
- 1981
This is why the correction to the Weizsäcker functional is often made using the Pauli potential [23, 24, 52, 53]. It is interesting, and disappointing, that even though the Weizsäcker model for the density matrix, ( 2.32 ), is very simple, the quasiprobability distribution cannot generally be expressed in closed form, even for the simplest g ( θ , τ )=1 case (corresponding to the Wigner ...
The energy values thus obtained are compared with the exact quantum mechanical values, and it is shown that the Weizsäcker term is too large in its original form and a weighting factor λ≈1/5 (in contrast to the Kirzhnits' conclusion λ≈1/9) is necessary to give a substantial improvement over the Thomas-Fermi solution.
- Katsumi Yonei, Yasuo Tomishima
- 1965
