From 39fc4f068a2f80c3b0af5d2d2bfed702baefb8dc Mon Sep 17 00:00:00 2001 From: pkirwin Date: Mon, 1 Mar 2021 17:02:24 -0700 Subject: [PATCH] commit --- PS2/doc.aux | 2 +- PS2/doc.fdb_latexmk | 14 ++++++++------ PS2/doc.fls | 14 ++++++++++++++ PS2/doc.log | 27 +++++++++++++++++++-------- PS2/doc.pdf | Bin 307787 -> 346266 bytes PS2/doc.synctex.gz | Bin 99874 -> 101835 bytes PS2/doc.tex | 25 ++++++++++++++++++++++--- 7 files changed, 64 insertions(+), 18 deletions(-) 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). 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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}