Quantum solid-state physics
Quantum solid-state physics
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量子固体物理
DOI：
10.1007/978-3-642-50164-7
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
M. Katsnelson
中科院分区：
文献类型：
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作者：
S. Vonsovsky;M. Katsnelson;M. Katsnelson
固体的量子理论在现代理论物理学的总体结构中占有特殊而重要的地位。目前没有理由质疑这样一种说法，即固体的所有性质原则上都可以在量子力学和统计力学的牢固建立的基础上得到解释。然而，真实的固体的这些性质和一般物质的凝聚态是如此复杂和多样，以至于至少在目前，几乎不可能从第一原理严格和充分地解释晶体的观察到的特性，即使是那些接近完美的晶体，更不用说解释它们存在的事实了！因此，除了应用于理论物理学其他更基本领域的数学方法和物理概念外，固态理论还发展了自己的方法来解释各种物质的最重要性质。值得注意的是，这些方法现在不仅对统计物理学，而且对粒子物理学，甚至对天体物理学和宇宙学产生了深刻的相互影响。除此之外，还必须注意到固体理论的巨大和日益增长的应用意义。在此只需提及半导体器件理论、强度和塑性理论、材料磁性理论等。在这方面，现代固体理论在实践中取得了巨大成功，它采用了足够简单的理论背景，基于纯粹的现象学方法和微观模型，这些模型在数学上相对简单，在物理上非常清晰。如上所述，完全实现“第一原理”的固体量子理论，即固体的所有性质都来自于单个组成原子的性质的理论，是不存在的。然而，我们可以假设，例如，现在在简单（正常）金属理论中得到广泛应用的赝势方法无疑取得了相当大的成功，这是朝着构建这样一个物理上一致的第一性原理理论迈出的重要一步。因此，在本文中，我们没有选择演绎的方法，而是选择了一种基于对简单的固体经验性质的处理和分析的方法，只有在必要时才诉诸更复杂的模型。在某种程度上，这样的论述再现了现代理论物理学这一重要领域的演变（在这方面不同于专门讨论有关问题的各种专著和教科书），而且在我们看来，最适合于引导读者进入这一主题。我们还假设，详细讨论一些经典问题，如具有周期势的一维薛定谔方程、金属-绝缘体判据、电场和磁场对电子态的影响，以及其他类似问题，将是非常有益的。同时，这本书提出了一些最新的主题：由晶格，等离子体和费米液体效应，赝势理论的元素，无序系统的理论基础，中子散射等。
The quantum theory of solids occupies a peculiar and important place in the general structure of modern theoretical physics. There are currently no grounds for questioning the statement that all properties of solids can, in principle, be accounted for on the basis of firmly established principles of quantum and statistical mechanics. Nevertheless, these properties of real solids and the condensed state of matter in general, are so complicated and diverse that it is well nigh impossible, at least at present, to explain rigorously and fully from first principles the observed characteristics of crystals, even those which are close to perfect,-let alone explain the fact that they exist! Therefore, alongside the mathematical methods and physical concepts applied in other more fundamental areas of theoretical physics, solid state theory has developed approaches of its own to account for the most important properties of the various substances. Significantly, these approaches now have a profound reciprocal effect on not only statistical physics but also on particle physics, and even on astrophysics and cosmology. Apart from this, the tremendous and ever-increasing applied significance of solid-state theory must be noted. Suffice it to mention here the theory of semiconducting devices, the theory of strength and plasticity, the theory of magnetic properties of materials, etc. In this respect, modern solid-state theory employs with great practical success a sufficiently simple and, at the same time, adequate theoretical background, based on a purely phenomenological approach and microscopic models that are comparatively simple in terms of mathematics and very lucid physically.As stated above, a quantum theory of solids that realizes the “first-principles” program in its entirety, ie, a theory in which all properties of solid are derived from those of individual constituent atoms, does not exist. However it may well be assumed that, for example, the indubitable and sizable success of the pseudopotential method that now enjoys wide use in the theory of simple (normal) metals is an important step toward the construction of such a physically consistent first principles theory. Rather than choosing the deductive method of presentation, we have therefore opted, in this text, for a method based on a treatment and analysis of simple empirically established properties of solids, resorting to more соmplicated models only where necessary. In a way, such an exposition reproduces the evolution of this important province of modern theoretical physics (differing in this respect from the diverse monographs and textbooks devoted to the problem concerned) and, in our view, is most appropriate to initiate the reader into the subject. We have also assumed that a detailed treatment of a number of classical topics such as the one-dimensional Schródinger equation with a periodic potential, the metal-insulator criterion, the effect of electric and magnetic fields on electronic states, and other similar problems would be very instructive. At the same time, the book presents a number of up-to-date topics: the scattering of neutrons by the crystal lattice, plasma and Fermi liquid effects, elements of pseudopotential theory, fundamentals of the theory of disordered systems, etc.