Leading corrections to local approximations II : The case with turning points
Leading corrections to local approximations II : The case with turning points
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对局部近似的领先修正二：有转折点的情况
DOI：
10.1103/physrevb.95.115115
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发表时间：
2016
影响因子：
3.7
通讯作者：
K. Burke
中科院分区：
文献类型：
--
作者：
R. Ribeiro;K. Burke
研究了在密度和动能均为半经典近似下，无相互作用的一维费米子的TF理论的量子修正。它们的结构进行了分析，并从不同的相空间区域（经典允许与禁止在费米能量）的贡献解析。导出了每个区域的粒子数和能量分量的普适公式。例如，在半经典极限下，在转折点之后，恰好有1/（6\pi 3 ^{1/2}）的粒子泄漏到消逝区。在半经典极限下，用解析方法证明了半经典密度的正确归一化。能量和密度的测试数值在各种一维的潜力，特别是在TF理论成为精确的极限。探讨了半经典近似的逐点精度与积分期望值之间的微妙关系。当势变化太快时，半经典公式的局限性也被研究。的近似示出的多个威尔斯井，除了在中间的相位点的倏逝区域。密度泛函近似的影响进行了讨论。
Quantum corrections to Thomas-Fermi (TF) theory are investigated for noninteracting one-dimensional fermions with known uniform semiclassical approximations to the density and kinetic energy. Their structure is analyzed, and contributions from distinct phase space regions (classically-allowed versus forbidden at the Fermi energy) are derived analytically. Universal formulas are derived for both particle numbers and energy components in each region. For example, in the semiclassical limit, exactly 1/(6\pi3^{1/2}) of a particle leaks into the evanescent region beyond a turning point. The correct normalization of semiclassical densities is proven analytically in the semiclassical limit. Energies and densities are tested numerically in a variety of one-dimensional potentials, especially in the limit where TF theory becomes exact. The subtle relation between the pointwise accuracy of the semiclassical approximation and integrated expectation values is explored. The limitations of the semiclassical formulas are also investigated when the potential varies too rapidly. The approximations are shown to work for multiple wells, except right at the mid-phase point of the evanescent regions. The implications for density functional approximations are discussed.