ELECTRONS IN LATTICE FIELDS
ELECTRONS IN LATTICE FIELDS
复制标题
DOI：
10.1080/00018735400101213
复制
发表时间：
1954-01-01
影响因子：
--
通讯作者：
FROHLICH, H
中科院分区：
文献类型：
--
作者：
FROHLICH, H
讨论这一问题的意义是双重的。当然，首先，计算离子晶体中自由电子的性质具有内在的意义。然而，第二，这种情况为非相对论性场论提供了一个非常简单的例子，鉴于它的简单性，它可能会导致发现这种场的许多新特征和发展新方法。事实上，在第一次将场论方法应用于离子晶体中的电子之后（FrShlieh，佩尔泽和Zienau，1950），这些方法在金属中的应用导致了超导理论的重要一步，并导致了同位素效应的预测（Fr 6 hlich，1950）。然而，随后的讨论表明（FrShlieh 1953），需要新的方法来处理超导性的所有方面，目前看来，一种将§ 4和§ 5中描述的两种方法的结果结合起来的方法可能符合要求。第6节结束）。§ 4和§ 5的方法可以分别最好地描述为动态和静态。静力法实质上是Hartree自洽场法的一种应用。因此，离子晶格中质量为m的电子可以用电子波函数来描述，该电子波函数产生平均电荷分布p。将该p视为静电荷，它在晶格中建立了极化，该极化可以根据静电定律计算。这种极化产生了对电子的吸引力，如果电荷p在半径为1的球形范围内延伸，则势能为e2/le*; E* 是有效介电常数。电子在空间中的限制要求它的德布罗意布罗意波长是1的量级，所以它的Z ′ 2
The interest in discussing this question is twofold. Firstly, of course, a calculation of the properties of free electrons in ionic crystals has an intrinsic interest. Secondly, however, this case provides a very simple example for a non relativistic field theory, and in view of its simplicity it might be expected to lead to the discovery of a number of new features of such fields and to the development of new methods. In fact after the first, application of the methods of field theory to electrons in ionic crystals (FrShlieh, Pelzer and Zienau 1950), the use of these methods in metals led to an important step in the theory of superconductivity and to the prediction of the isotope effect (Fr6hlich 1950). Subsequent discussion has shown, however (FrShlieh 1953) that new methods are required to deal with all aspects of superconductivity, and at present it seems that, a method which wouldcombine the results of the two methods described in § 4 and § 5 might fit the requirements (cf. end of § 6). The methods of § 4 and § 5 can best be described as dynamic and static respectively. The static method is essentially an application of Hartree's self consistent field method. Thus an electron with mass m in an ionic lattice may be described by an electronic wave function giving rise to an average charge distribution p. Treating this p as a static charge, it establishes a polarization in the lattice which can be calculated from the laws of electrostatics. This polarization gives rise to an attractive force on the electron, and to a potential energy of the order--e2/le* if the charge p extends over a spherical range whose radius is of the order 1; E* is an effective dielectric constant. The restriction of the electron in space requires its de Broglie wave length to be of the order 1 so"~ hat its Z'2