SELF-CONSISTENT FIELD APPROACH TO THE MANY-ELECTRON PROBLEM
SELF-CONSISTENT FIELD APPROACH TO THE MANY-ELECTRON PROBLEM
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DOI：
10.1103/physrev.115.786
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发表时间：
1959-01-01
期刊：
影响因子：
--
通讯作者：
COHEN, MH
中科院分区：
文献类型：
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作者：
EHRENREICH, H;COHEN, MH
用单电子与自洽电磁场的含时相互作用来描述多电子系统的自洽场方法在许多方面与Sawada和Brout的处理方法是等价的。从正确的多电子哈密顿量出发，当采用Sawada-Brout方案的近似特征时，发现在自洽场框架下，对产生算符的运动方程与单粒子密度矩阵的运动方程是相同的。这些近似被认为对应于(1)两粒子密度矩阵的因式分解，以及(2)相对于单粒子密度矩阵的非对角分量的线性化。对于自由电子气和真实固体，复数的频率相关介电常数都是由自洽场方法直接求出的。它与Noziéres和Pines在随机位相近似下得到的结果相同。讨论了固体在长波极限下的等离子体色散关系。
The self-consistent field method in which a many-electron system is described by a time-dependent interaction of a single electron with a self-consistent electromagnetic field is shown to be equivalent for many purposes to the treatment given by Sawada and Brout. Starting with the correct many-electron Hamiltonian, it is found, when the approximations characteristic of the Sawada-Brout scheme are made, that the equation of motion for the pair creation operators is the same as that for the one-particle density matrix in the self-consistent field framework. These approximations are seen to correspond to (1) factorization of the two-particle density matrix, and (2) linearization with respect to off-diagonal components of the one-particle density matrix. The complex, frequency-dependent dielectric constant is obtained straight-forwardly from the self-consistent field approach both for a free-electron gas and a real solid. It is found to be the same as that obtained by Noziéres and Pines in the random phase approximation. The resulting plasma dispersion relation for the solid in the limit of long wavelengths is discussed.