Abstract
One common feature of most derivations of the gradient expansion for the kinetic energy density is the use of a mock phase space in intermediate steps. By mock phase space I mean a space parametrized by two coordinates p and r which in the classical limit reduce to the classical phase space. Of course a real phase space can not be defined quantum mechanically since p and r can not be specified simultaneously. Also there are many different mock phase spaces of which two in particular are frequently used. We will discuss these two in detail later. I will begin by giving a brief derivation of the Thomas-Fermi relation between the kinetic energy density and the spatial density to motivate the use of phase space and then indicate how this must be generalized. I then will discuss the various quantum mechanical generalizations of the phase space and show using the Wigner transform as an example one method of obtaining an ħ expansion. More details can be found in a review article by N.L. Balazs and myself.1
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References
N.L. Balazs and B.K. Jennings, TRIUMF preprint TRI-PP-83–55 (submitted to Physics Reports).
E.K.U. Gross, this proceedings.
D.A. Kirzhnits, Field Theoretical Methods in Many-Body Systems, Pergamon, Oxford (1967).
J.G. Kirkwood, Phys. Rev. 44: 31 (1933).
A. Voros, Doctoral thesis, ORSAY (1977), unpublished.
B. Grammaticos and A. Voros, Ann. Phys. (N.Y.) 123: 359 (1979).
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© 1985 Plenum Press, New York
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Jennings, B.K. (1985). Gradient Expansions and Quantum Mechanical Extensions of the Classical Phase Space. In: Dreizler, R.M., da Providência, J. (eds) Density Functional Methods In Physics. NATO ASI Series, vol 123. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0818-9_18
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DOI: https://doi.org/10.1007/978-1-4757-0818-9_18
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