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Matalien l\"amp\"otilojen fysiikan teoria (Kyl-0.104)\hfil Autumn 2000\break
Electronic transport in mesoscopic systems\hfil Exercise set 7\break
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Exercise E.3.3 from Datta's book. Note that if we insist that the discretized version
reduces correctly to the continuum case when $a\rightarrow 0$, then eq. (3.5.18)
should read ($t=\hbar^2/2ma^2$)
$$g_p^R(p_i,p_j)= -{1\over at}\sum_m\chi_m(p_i)\exp({\rm i}k_ma)\chi_m(p_j).$$
(Datta neglects factors of $a$ in the delta function.)
Also, I find this result more simple to derive by adding a reflected wave to
the solution of an infinite lead. There are also some sign mistakes in Datta's
solution. Also justify, why the truncation problem leads to consider a semi-infinite
lead. 
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Exercises E.3.4 - E.3.6 from Datta's book. 
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