Lector notes on lattice and its types of lattice physics
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A lecture note on the lattice waves in the solid is presented. In a crystal each atom are coupled with the neighboring atoms by spring constants. The collective motion of atoms leads to a well-defined traveling wave over the whole system, leading to the collective motion, so called phonon. Here the equation of motion of atoms around thermal equilibrium position will be discussed in terms of several methods, which include numerical calculation on the eigenvalue problem (based on the Mathematica) and the translation operators in the quantum mechanics. We show that all these methods lead to the same conclusion, the existence of lattice wave, phonon in the quantum mechanics. For students who just start to study the solid state physics, it may be difficult to understand the validity of the assumption that the deviation of the displacement of the atoms from the thermal equilibrium is well described by a traveling wave. We numerically solve the eigenvalue-problem of the motion of atoms in the linear chain (typically 50-100 atoms) using Mathematica. We will give a bit of evidence for the existence of the normal modes propagating along the linear chain. This is a part of lecture note on solid state physics (Phys.472/572) at the SUNY at Binghamton (see the detail at the following URL