By Solyom J.
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Extra resources for Fundamentals of the Physics of Solids: Volume 1: Structure and Dynamics
If the orientation of the crystallographic axes is the same throughout the sample then the sample is called a single crystal. In real crystals, however, the order is never perfect. First, there may be defects in the atomic arrangement due to imperfect crystal growth, and these defects can destroy the correlation between the positions of distant atoms. 2 Classiﬁcation of Condensed Matter According to Structure 21 grow at several points then the sample will consist of crystal grains of diﬀerent (usually macroscopic) sizes and irregular shapes, so-called crystallites.
Schrödinger, 1926. Erwin Schrödinger (1887–1961) shared the Nobel Prize with Paul Adrien Maurice Dirac (1902–1984) in 1933 “for the discovery of new productive forms of atomic theory”. 7) i=j which is commonly used in the literature even today. Up to this point, the above Hamiltonian can equally well describe a gas, a plasma, a liquid, or a solid. In gases and liquids our task is much simpler as electrons do not move around freely but are bound to nuclei. Now interactions are relatively weak between neutral atoms or molecules, which can be considered as the new elementary units.
At the end of the chapter we shall present a derivation of the corresponding term in the Hamiltonian. 3 Relativistic Eﬀects When writing down the previous form of the Hamiltonian it was tacitly assumed that relativistic eﬀects can be ignored. More precisely, it was taken into account that electrons have a spin – but apart from that the Schrödinger equation of nonrelativistic quantum mechanics was used. 4 However, these eﬀects can be observed for electrons moving in the ﬁeld of 2 3 4 Throughout the book, we follow the convention that s and l are dimensionless quantities for the electron’s intrinsic angular momentum (spin) and orbital angular momentum.