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Oscillations in Systems with Many Particles: Standing Waves

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Book Id: WPLBN0000686533
Format Type: PDF eBook
File Size: 202.02 KB.
Reproduction Date: 2005
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Title: Oscillations in Systems with Many Particles: Standing Waves  
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Language: English
Subject: Science., Physics, Physics--Research
Collections: Physics Literature
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Oscillations in Systems with Many Particles: Standing Waves. (n.d.). Oscillations in Systems with Many Particles: Standing Waves. Retrieved from http://www.worldebooklibrary.org/


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Physics Literature

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Introduction: Our discussion in the previous chapter shows that the calculation of normal modes in a vibrating system becomes more and more difficult as the number of masses increases. It appears that for real systems such as crystals, which have as many as 1023 atoms/cm3, no supercomputer will ever be able to calculate the normal modes of vibration. However, we hinted at a possible solution of this problem for systems that have some type of symmetry. Crystals do display a very special type of symmetry: they have a pattern that repeats itself throughout the structure. These systems are called periodic. In this chapter, we will show that the calculation of normal modes in a periodic one-dimensional crystal is surprisingly simple. In fact, we will solve the problem once and forever: our solution will be valid for any number N of masses. The periodicity of these systems is reflected in their normal mode solutions, which display themselves a periodicity: masses separated by a certain distance execute exactly the same motion.

 

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