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%physical constants in MKS units
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hbar = 1.054e-34;
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q = 1.602e-19;
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m = 9.110e-31;
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%generate lattice
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N = 100; %number of lattice points
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n = [1:N]; %lattice points
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a = 1e-10; %lattice constant
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x = a * [1:1:N];
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@ -1,12 +1,14 @@
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# Fdb version 3
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# Fdb version 3
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["pdflatex"] 1614634922 "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf" "doc" 1614634924
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@ -23,6 +25,7 @@
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@ -74,13 +77,13 @@
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"doc.aux" 1614629797 32 4d1825978335c8847f72f7c473f9edc8 "pdflatex"
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"doc.aux" 1614634924 32 4d1825978335c8847f72f7c473f9edc8 "pdflatex"
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"doc.tex" 1614629794 5381 757cb104f3b17ae2bba772ec8fa8e743 ""
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"doc.tex" 1614634921 5526 6265d6def36657f58ffe0e5a11340609 ""
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(generated)
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(generated)
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"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf"
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"doc.aux"
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"doc.log"
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"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.log"
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"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf"
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@ -471,11 +471,21 @@ INPUT C:\Users\speed\AppData\Local\MiKTeX\pdftex\config\pdftex.map
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INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm5.tfm
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INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux
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INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux
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INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmbx10.pfb
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INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\type1\public\amsfonts\cm\cmbx10.pfb
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This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 21.1) (preloaded format=pdflatex 2021.2.6) 1 MAR 2021 13:16
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This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 21.1) (preloaded format=pdflatex 2021.2.6) 1 MAR 2021 14:42
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entering extended mode
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entering extended mode
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**d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex
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**d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex
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(d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex
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(d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex
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{C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map}] [2] [3] [4] [5] [6] [7] (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) )
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{C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map}] [2] [3] [4] [5] [6] [7] (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) )
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7326 strings out of 479618
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<C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmbx10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmbx12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr17.pfb>
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<C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmbx10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmbx12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr12.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr17.pfb>
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Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (7 pages, 75208 bytes).
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Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (7 pages, 85838 bytes).
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PDF statistics:
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PDF statistics:
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46 PDF objects out of 1000 (max. 8388607)
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50 PDF objects out of 1000 (max. 8388607)
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1 words of extra memory for PDF output out of 10000 (max. 10000000)
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\begin{enumerate}[align=left,leftmargin=*,labelsep=1em,label=\bfseries(\alph*)]
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\begin{enumerate}[align=left,leftmargin=*,labelsep=1em,label=\bfseries(\alph*)]
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\item %1a
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\item %1b
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\begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)]
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The analytical solution is
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\begin{equation}
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\item %1ci
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\item %1ci
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