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Full-Text Articles in Physical Sciences and Mathematics
Hellmann-Feynman Theorem In Thomas-Fermi And Related Theories, Jerry Goodisman
Hellmann-Feynman Theorem In Thomas-Fermi And Related Theories, Jerry Goodisman
Chemistry - All Scholarship
The general Hellmann-Feynman theorem (derivative of energy with respect to a parameter = expectation value of derivative of Hamiltonian) is proved for theories in which the electron density is determined by making the energy functional stationary. Some simple applications are given.
Modified Weizsäcker Corrections In Thomas-Fermi Theories, Jerry Goodisman
Modified Weizsäcker Corrections In Thomas-Fermi Theories, Jerry Goodisman
Chemistry - All Scholarship
We consider theories in which a kinetic-energy correction (h2322m)[2] (=density) is added to the usual Thomas-Fermi term. A treatment based on the WKB method and expected to be valid for large r shows =1 here, as found experimentally. For small r, =1 is needed to give proper behavior of, but other arguments suggest that the Thomas-Fermi term be dropped here.
Modified Quantum-Statistical Calculations For Atomic Electron Densities, Jerry Goodisman
Modified Quantum-Statistical Calculations For Atomic Electron Densities, Jerry Goodisman
Chemistry - All Scholarship
We attempt to overcome one of the shortcomings in the Thomas-Fermi and related theories for atoms by connecting a quantum-mechanical electron density for the region near the nucleus to a density given by a statistical model. The joining may be done in a nonarbitrary manner: All parameters are determined. It suffices to use a very crude and easily calculated approximation to the density to start with, so the calculation is quite easy. The resulting electron density is in much better agreement with reality than that from the unmodified theories.