## Question

###### Extra credit, very super hard! Consider set of N IaSSCS mwhich are still all equaL, but COHectexl by springs which alternate M Valuc: k.2k,k,2k.k Compute tic nOrIA] modes Ac hence the relation betWecn ald q. You will itucd (it'$ hard?) tat there are actually two typGs of modes. One is calledl acoustic phonons' aId the other is cllc| opticnl phonons' The algehra in this problem is also sitpl Model ol |d g"p)S for electrons HOving i solid like polvacetylene (a dimerizee chain o

Extra credit, very super hard! Consider set of N IaSSCS mwhich are still all equaL, but COHectexl by springs which alternate M Valuc: k.2k,k,2k.k Compute tic nOrIA] modes Ac hence the relation betWecn ald q. You will itucd (it'$ hard?) tat there are actually two typGs of modes. One is calledl acoustic phonons' aId the other is cllc| opticnl phonons' The algehra in this problem is also sitpl Model ol |d g"p)S for electrons HOving i solid like polvacetylene (a dimerizee chain of carhon atoms) wlcre the distances hetWecn aljacemt carhon atoms alternates 6om short t0 long; AIlc Ience (e ability ol electrons (0 'hop from carbon t0 carbon alternates betwevn casy and hard: So it's nice problem t0 master.

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