Corrections to Thomas-Fermi densities at turning points and beyond

Abstract

Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many non-interacting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the leading corrections to Thomas-Fermi theory, involve neither sums nor derivatives, are spatially uniform approximations, and are exceedingly accurate.

arXiv comment5 pages, 5 figures

References in corpus (4)

• Leading corrections to local approximations
• Potential functionals versus density functionals
• Closed-Orbit Theory of Spatial Density Oscillations in Finite Fermion Systems
• Semiclassical theory for spatial density oscillations in fermionic systems

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• Systematic corrections to the Thomas-Fermi approximation without a gradient expansion
• Leading corrections to local approximations II (with turning points)
• Airy-averaged gradient corrections for two-dimensional fermion gases
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• First-principles quantum corrections for carrier correlations in double-layer two-dimensional heterostructures
• Deriving approximate functionals with asymptotics
• Approximate normalizations for approximate density functionals
• Airy gas model: From three to reduced dimensions
• Asymptotics of eigenvalue sums when some turning points are complex