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The,product,of,the,time,independent,stationary,wave,solution,and,time,dependent,oscillator,solution.,The,,,negatively,,,charged,,,plasma,,,is,,,formed,,,by,,,the,,,valence,,,electrons,,,of,,,the,,,free,,,electron,,,model,,,that,,,are,,,uniformly,,,distributed,,,over,,,the,,,interior,,,of,,,the,,,solid.,,,At,a,resonance,frequency,ω,p,{displaystyle,omega,{p}},,,called,the,plasma,frequency,,the,dielectric,function,changes,sign,from,negative,to,positive,and,real,part,of,the,dielectric,function,drops,to,zero.,which,,is,,the,,final,,solution,,for,,the,,free,,electron,,wave,,function.,,E,(,k,),=,ℏ,2,k,2,2,m,{displaystyle,E({mathbf,{k}})={frac,{hbar,^{2}k^{2}}{2m}}},,,.,E,,(,,k,,),,=,,ℏ,,2,,k,,2,,2,,m,,{displaystyle,,E({mathbf,,{k}})={frac,,{hbar,,^{2}k^{2}}{2m}}},,,,,.,,gives,the,traveling,plane,wave,solution.,

with,,,two,,,electrons,,,(one,,,of,,,each,,,spin),,,per,,,each,,,"quantum",,,of,,,the,,,phase,,,space,,,,Δ,,,V,,,Δ,,,k,,,=,,,(,,,2,,,π,,,),,,3,,,{displaystyle,,,Delta,,,VDelta,,,{mathbf,,,{k}}=(2pi,,,)^{3}},,,.,,,New,,York:,,Holt,,,Rinehart,,and,,Winston.,,ϵ,,(,,ω,,),,=,,D,,(,,ω,,),,ϵ,,0,,E,,(,,ω,,),,=,,1,,+,,P,,(,,ω,,),,ϵ,,0,,E,,(,,ω,,),,{displaystyle,,epsilon,,(omega,,)={frac,,{D(omega,,)}{epsilon,,{0}E(omega,,)}}=1+{frac,,{P(omega,,)}{epsilon,,{0}E(omega,,)}}},,.,,Please,help,improve,this,article,by,adding,citations,to,reliable,sources.,κ,,=,,i,,k,,x,,=,,i,,2,,m,,E,,x,,ℏ,,2,,{displaystyle,,kappa,,=ik{x}=i{sqrt,,{frac,,{2mE{x}}{hbar,,^{2}}}}},,.,,Introduction,to,Solid,State,Physics.,−,ℏ,2,2,m,∇,2,Ψ,(,r,,,t,),=,i,ℏ,∂,∂,t,Ψ,(,r,,,t,),{displaystyle,-{frac,{hbar,^{2}}{2m}}nabla,^{2}Psi,({mathbf,{r}},t)=ihbar,{frac,{partial,}{partial,t}}Psi,({mathbf,{r}},t)},.,

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