Find dispersion relation using periodicity

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Homework Help Overview

The problem involves a linear chain of particles connected by springs, focusing on finding the dispersion relation using the periodicity of the system. The context includes concepts from solid state physics and wave mechanics.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the meaning of the variables η2j, η2j+1, and 'q' as they relate to the problem. There is a focus on the implications of the periodicity and the mathematical expressions provided.

Discussion Status

The discussion is currently exploring the definitions and roles of specific variables in the problem setup. Some participants express confusion about the assignment and suggest seeking clarification from the professor, indicating a lack of consensus on the foundational concepts.

Contextual Notes

There is an indication that the problem may involve assumptions or definitions that are not fully understood by all participants, which could affect their ability to engage with the problem effectively.

Shafikae
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Ok so here's another problem that i just completely don't understand at all. Thanks for your help.

A linear chain consists of 2N equally spaced identical particles with mass m and speration a, coupled by springs with alternating constands k1 and k2. Use the periodicity of the system to find the dispersion relation and sketch the resulting function ω (q). Hint: Assume

η2j = [tex]\alpha[/tex]e^i[2jaq-ωt] , η2j+1 = βe^i[(2j+1)aq - ωt]
 
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What do η2j and η2j+1 represent? What does 'q' represent?
 
I don't know. This is what the professor assigned.
 
Ask your professor then.

How on Earth do you expect to show that η2j =[itex]\alpha[/itex] e^i[2jaq-ωt], if you have no idea what the variables η2j and 'q' represent?!
 

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