diff --git a/PS2/doc.aux b/PS2/doc.aux index 67e19b0..12f0e58 100644 --- a/PS2/doc.aux +++ b/PS2/doc.aux @@ -11,4 +11,4 @@ \newlabel{eq:Riemann_sum}{{6}{4}} \newlabel{eq:numerical_E}{{7}{4}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Analytic solution to numeric system, plotted.\relax }}{5}{}\protected@file@percent } -\gdef \@abspage@last{9} +\gdef \@abspage@last{10} diff --git a/PS2/doc.fdb_latexmk b/PS2/doc.fdb_latexmk index a230dda..1588bfb 100644 --- a/PS2/doc.fdb_latexmk +++ b/PS2/doc.fdb_latexmk @@ -1,5 +1,5 @@ # Fdb version 3 -["pdflatex"] 1614642209 "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" 1614642211 +["pdflatex"] 1614643264 "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" 1614643267 "C:/Users/speed/AppData/Local/MiKTeX/fonts/pk/ljfour/jknappen/ec/dpi600/tcrm1000.pk" 1614620319 11548 693fc704971bedc6e913b37b081cf40e "" "C:/Users/speed/AppData/Local/MiKTeX/miktex/data/le/pdftex/pdflatex.fmt" 1612675286 9293900 83195ab665706b6f706823352908aa95 "" "C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map" 1614638559 80909 eab91d9745dd2edfd62a31d53cd5fe15 "" @@ -95,18 +95,20 @@ "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/parskip/parskip.sty" 1592833306 4414 25631f9679adf750bac898538ededd61 "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/setspace/setspace.sty" 1324294077 22913 a27d7908fc6f0385466454a966a316eb "" "C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/titlesec/titlesec.sty" 1571240058 48596 2b6a95da931c07a430b1a61904aaa42d "" - "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.aux" 1614642211 594 16258d68357a6aa33c90988b15b0fec2 "" - "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" 1614642208 15328 6099e64f934d062967e02a10084db0a5 "" - "doc.aux" 1614642211 594 16258d68357a6aa33c90988b15b0fec2 "pdflatex" - "doc.tex" 1614642208 15328 6099e64f934d062967e02a10084db0a5 "" + "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.aux" 1614643267 595 b019f47a873e4d7577a5d1c178942da9 "" + "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" 1614643260 16400 c38e0dd0cf4d7c750a7961b5b02ff142 "" + "doc.aux" 1614643267 595 b019f47a873e4d7577a5d1c178942da9 "pdflatex" + "doc.tex" 1614643260 16400 c38e0dd0cf4d7c750a7961b5b02ff142 "" "q1a_1and50.png" 1614636283 34155 72f34c6abf061325ae1f162db0ffd06b "" "q1a_eigenvals.png" 1614637266 23078 9c99a5505761d0b964e665e35fd9c02a "" "q1cii.png" 1614640691 20581 6a6b3aa285fd3f5be369532a6d2a033d "" "q1civ_fig1.png" 1614640691 20825 3bcd72f9b5aa0ff86ec535618927b345 "" "q1civ_fig2.png" 1614640691 18950 09e638d39de7c71e3285b2507fc9bb06 "" + "q1di_fig1.png" 1614642205 23575 17449aebb9c23a5139435b3506cbca3d "" + "q1di_fig2.png" 1614642205 13867 650413e942c9c7a655204496b4f3c21b "" (generated) "doc.pdf" "doc.aux" "doc.log" - "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.log" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf" + "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.log" diff --git a/PS2/doc.fls b/PS2/doc.fls index 40ffa6c..13082a1 100644 --- a/PS2/doc.fls +++ b/PS2/doc.fls @@ -536,6 +536,20 @@ INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1civ_fig2.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1civ_fig2.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1civ_fig2.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig1.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig1.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig1.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig1.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig1.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig1.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig1.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig2.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig2.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig2.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig2.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig2.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig2.png +INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1di_fig2.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux INPUT C:\Users\speed\AppData\Local\MiKTeX\fonts\pk\ljfour\jknappen\ec\dpi600\tcrm1000.pk INPUT C:\Users\speed\AppData\Local\MiKTeX\fonts\pk\ljfour\jknappen\ec\dpi600\tcrm1000.pk diff --git a/PS2/doc.log b/PS2/doc.log index 7dcf3e2..1b295e0 100644 --- a/PS2/doc.log +++ b/PS2/doc.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 21.1) (preloaded format=pdflatex 2021.2.6) 1 MAR 2021 16:43 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 21.1) (preloaded format=pdflatex 2021.2.6) 1 MAR 2021 17:01 entering extended mode **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.tex @@ -349,19 +349,30 @@ File: q1civ_fig2.png Graphic file (type png) Package pdftex.def Info: q1civ_fig2.png used on input line 309. (pdftex.def) Requested size: 252.94499pt x 189.7102pt. - [5 ] [6 ] [7] [8] [9] (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) ) + [5 ] + +File: q1di_fig1.png Graphic file (type png) + +Package pdftex.def Info: q1di_fig1.png used on input line 334. +(pdftex.def) Requested size: 252.94499pt x 189.7102pt. + +File: q1di_fig2.png Graphic file (type png) + +Package pdftex.def Info: q1di_fig2.png used on input line 339. +(pdftex.def) Requested size: 252.94499pt x 189.7102pt. + [6 ] [7] [8] [9] [10] (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) ) Here is how much of TeX's memory you used: - 8355 strings out of 479618 - 125554 string characters out of 2865027 + 8367 strings out of 479618 + 125748 string characters out of 2865027 981750 words of memory out of 3000000 - 25417 multiletter control sequences out of 15000+200000 + 25427 multiletter control sequences out of 15000+200000 412866 words of font info for 64 fonts, out of 3000000 for 9000 1141 hyphenation exceptions out of 8191 68i,12n,75p,1278b,2408s stack positions out of 5000i,500n,10000p,200000b,50000s -Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (9 pages, 307787 bytes). +Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (10 pages, 346266 bytes). PDF statistics: - 107 PDF objects out of 1000 (max. 8388607) + 112 PDF objects out of 1000 (max. 8388607) 0 named destinations out of 1000 (max. 500000) - 26 words of extra memory for PDF output out of 10000 (max. 10000000) + 36 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/PS2/doc.pdf b/PS2/doc.pdf index 67fa4ca..03785e4 100644 Binary files a/PS2/doc.pdf and b/PS2/doc.pdf differ diff --git a/PS2/doc.synctex.gz b/PS2/doc.synctex.gz index 87adc58..a2fffc4 100644 Binary files a/PS2/doc.synctex.gz and b/PS2/doc.synctex.gz differ diff --git a/PS2/doc.tex b/PS2/doc.tex index 60ae7f5..98ce2a1 100644 --- a/PS2/doc.tex +++ b/PS2/doc.tex @@ -314,27 +314,46 @@ legend({'Numerical','Analytical'},'Location','northwest'); % TODO idk if this is enough With the decreased lattice spacing, and increased number of points, we can see the numerical solution of eigenvalues matches the analytical solution much closer. As well, we can see that the probability - density function appears to be "squeezed" in the centre, for the $n = 50$ case. + density function appears to be "squeezed" in the centre, for the $n = 50$ case. The \(n=50\) case is + now a constant-amplitude wave, which corresponds to the expected analytic result - in contrast to the + plot in section (a), which has a low-frequency envelope around it. \end{enumerate} \item %1d \begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)] \item %1di - + In order to modify the computations to those for a particle in a "ring" we simply had to add $-t_0$ elements as the "corner" elements of the hamiltonian operator array. - % TODO do we need a listing here + \begin{figure}[H] + \centering + \begin{subfigure}{0.5\textwidth} + \centering + \includegraphics[width=\textwidth]{q1di_fig1.png} + \caption{Probability densities for \(n=4\)\\and \(n=5\).} + \end{subfigure}% + \begin{subfigure}{0.5\textwidth} + \centering + \includegraphics[width=\textwidth]{q1di_fig2.png} + \caption{Comparison of first 101 numerical and analytic eigenvalues.} + \end{subfigure} + \end{figure} \item %1dii + The energy levels for eigenvalues number 4 and 5 are both $0.06eV$. + Because these eigenstates both have the same eigenvalue (0.06). \item %1diii + % TODO add figure for sketch \item %1div + + \end{enumerate}