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Hermitian one-particle density matrix through a semiclassical gradient expansion

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Original languageEnglish
Article number015205
JournalJournal of Physics A: Mathematical and Theoretical
Issue number1
Publication statusPublished - 9 Dec 2015
Publication typeA1 Journal article-refereed


We carry out the semiclassical expansion of the one-particle density matrix up to the second order in h. We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.


  • density matrix, density-functional theory, Wigner transform

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Field of science, Statistics Finland