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CondMat07PS6 - 1 CONDENSED MATTER PHYSICS 171.405 171.621...

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1 CONDENSED MATTER PHYSICS 171.405 / 171.621 Instructor: N.P. Armitage Grader: Paula Mellado Fall 2007 Problem Set 5 Due to Graders mail box by Monday Dec. 10th ============================= Q 1: Kittel Problem 4.1 ============================= Q 1: Kittel Problem 4.3 ============================= Q 2: In class we solved the equations of motion for the linear diatomic chain and found two solutions for its atomic motion. These are referred to as acoustic and optical phonon branches. Two branches exist because we allowed motion in only one direction and there are two atoms per unit cell. In other words, for 1D motion, in order for there to be two branches there MUST be two different atoms per unit cell. In principle these two different atoms can differ in a variety of ways including having different masses only (for instance different isotopes), different charges only (different ions), both different masses and charges, or other distinctions. Consider the case where the masses are almost exactly the same, but they have different charges. The different charges allows a dipole moment, so that optical phonons can be excited optically. As it is only the ion masses that
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