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{\LARGE \ Physics 861 -- Fall 00}

{\bf Problem set 11 - }Due Thursday, Dec 6\bigskip 
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\noindent {\bf 1. }

Show that the Lindhard dielectric constant $\varepsilon ({\bf q},\omega )$,
given for instance by eq. (17.60) in Ashcroft-Mermin, reduces to $1-\omega
_{p}^{2}/\omega ^{2}$ in the limit $q\rightarrow 0$ at finite $\omega $.
Obtain the next-order correction in $q$, which is of order $q^{2}$. Find the
(bulk) plasmon dispersion relation, to order $q^{2}$. How does this $q^{2}$
term in $\varepsilon ({\bf q},\omega )$ affect the surface plasmon-polariton
dispersion relation discussed in homework 1?

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\noindent {\bf 2. }

(a) Problem 4, page 352 of Ashcroft-Mermin.

(b) Same problem, but using the screened Coulomb potential (Thomas-Fermi
screening).

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\noindent {\bf 3. }

Problem 1, page 486, of Ashcroft-Mermin

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