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Corrections to Thomas-Fermi densities at turning points and beyond
Raphael F Ribeiro1, Donghyung Lee2, Attila Cangi3
1Department of Chemistry, University of California, Irvine, California 92697, USA.
Physical Review Letters
|February 21, 2015
Summary
New semiclassical approximations accurately estimate densities for many noninteracting fermions in one-dimensional potentials. These findings offer leading corrections to Thomas-Fermi theory without complex calculations.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- Thomas-Fermi theory provides a basic approximation for electron density in quantum systems.
- Accurate density calculations are crucial for understanding material properties.
- Previous methods often involve complex summations or derivatives.
Purpose of the Study:
- To derive uniform semiclassical approximations for number and kinetic-energy densities.
- To develop simple, closed-form expressions for these densities.
- To provide leading corrections to Thomas-Fermi theory.
Main Methods:
- Derivation of semiclassical approximations for noninteracting fermions.
- Focus on one-dimensional potentials with two turning points.
- Development of spatially uniform approximations.
Main Results:
- Simple, closed-form expressions for number and kinetic-energy densities were obtained.
- The expressions include leading corrections to Thomas-Fermi theory.
- The approximations are spatially uniform and highly accurate, avoiding sums and derivatives.
Conclusions:
- The derived uniform semiclassical approximations offer a significant improvement over Thomas-Fermi theory.
- These approximations provide accurate and computationally efficient methods for density estimation.
- The findings are applicable to many-fermion systems in specific one-dimensional potentials.
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