david/ECE_456_Reports
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

commit

Browse Source
This commit is contained in:
pkirwin 2021-03-01 20:21:04 -07:00
parent 5b01c21e10
commit 8b7754bd2b
8 changed files with 95 additions and 68 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
PS2/doc.aux
View File

@ -4,6 +4,7 @@
\newlabel{sub@fig:q3_ne}{{a}{3}} \newlabel{sub@fig:q3_ne}{{a}{3}}
\newlabel{fig:q3_current}{{1b}{3}} \newlabel{fig:q3_current}{{1b}{3}}
\newlabel{sub@fig:q3_current}{{b}{3}} \newlabel{sub@fig:q3_current}{{b}{3}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces (a) Probability densities for \(n=1\) and \(n=50\). (b) Comparison of first 101 numerical and analytic eigenvalues.\relax }}{3}{}\protected@file@percent }
\newlabel{eq:analytical}{{1}{3}} \newlabel{eq:analytical}{{1}{3}}
\newlabel{eq:normalise}{{2}{3}} \newlabel{eq:normalise}{{2}{3}}
\newlabel{eq:integral_ident}{{3}{3}} \newlabel{eq:integral_ident}{{3}{3}}
@ -12,4 +13,5 @@
\newlabel{eq:numerical_E}{{7}{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 } \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Analytic solution to numeric system, plotted.\relax }}{5}{}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Sketch of appropriate energy levels\relax }}{7}{}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Sketch of appropriate energy levels\relax }}{7}{}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Numerical result (black line) and analytical solution scaled by \(a\) (orange circles).\relax }}{10}{}\protected@file@percent }
\gdef \@abspage@last{12} \gdef \@abspage@last{12}

17
PS2/doc.fdb_latexmk
View File

@ -1,5 +1,5 @@
# Fdb version 3 # Fdb version 3
["pdflatex"] 1614653239 "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" 1614653243 ["pdflatex"] 1614655256 "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" 1614655259
"C:/Users/speed/AppData/Local/MiKTeX/fonts/pk/ljfour/jknappen/ec/dpi600/tcrm1000.pk" 1614620319 11548 693fc704971bedc6e913b37b081cf40e "" "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/miktex/data/le/pdftex/pdflatex.fmt" 1612675286 9293900 83195ab665706b6f706823352908aa95 ""
"C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map" 1614638559 80909 eab91d9745dd2edfd62a31d53cd5fe15 "" "C:/Users/speed/AppData/Local/MiKTeX/pdftex/config/pdftex.map" 1614638559 80909 eab91d9745dd2edfd62a31d53cd5fe15 ""
@ -97,10 +97,10 @@
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/parskip/parskip.sty" 1592833306 4414 25631f9679adf750bac898538ededd61 "" "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/setspace/setspace.sty" 1324294077 22913 a27d7908fc6f0385466454a966a316eb ""
"C:/Users/speed/AppData/Local/Programs/MiKTeX/tex/latex/titlesec/titlesec.sty" 1571240058 48596 2b6a95da931c07a430b1a61904aaa42d "" "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" 1614653242 740 9ca5a038ed4ac5ccabd4bb4170e5688b "" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.aux" 1614655259 1163 a0354534513b31cd9af2bee0ca4d6d1a ""
"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" 1614653238 20515 ff9dd2e9b5270ae7d092432224a524d8 "" "d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.tex" 1614655255 21406 c34edfd6306342301c6d3fe25c1a3804 ""
"doc.aux" 1614653242 740 9ca5a038ed4ac5ccabd4bb4170e5688b "pdflatex" "doc.aux" 1614655259 1163 a0354534513b31cd9af2bee0ca4d6d1a "pdflatex"
"doc.tex" 1614653238 20515 ff9dd2e9b5270ae7d092432224a524d8 "" "doc.tex" 1614655255 21406 c34edfd6306342301c6d3fe25c1a3804 ""
"q1a_1and50.png" 1614636283 34155 72f34c6abf061325ae1f162db0ffd06b "" "q1a_1and50.png" 1614636283 34155 72f34c6abf061325ae1f162db0ffd06b ""
"q1a_eigenvals.png" 1614637266 23078 9c99a5505761d0b964e665e35fd9c02a "" "q1a_eigenvals.png" 1614637266 23078 9c99a5505761d0b964e665e35fd9c02a ""
"q1cii.png" 1614640691 20581 6a6b3aa285fd3f5be369532a6d2a033d "" "q1cii.png" 1614640691 20581 6a6b3aa285fd3f5be369532a6d2a033d ""
@ -111,9 +111,10 @@
"q1div.jpg" 1614643890 3254255 657a32881fc66c752988aa2be34fe320 "" "q1div.jpg" 1614643890 3254255 657a32881fc66c752988aa2be34fe320 ""
"q2c_fig1_1s.png" 1614652840 23989 50364061f25cfea80c735ce05ba391dd "" "q2c_fig1_1s.png" 1614652840 23989 50364061f25cfea80c735ce05ba391dd ""
"q2c_fig2_2s.png" 1614652829 29139 9c3bdf9df7dc973686f5105c04140b36 "" "q2c_fig2_2s.png" 1614652829 29139 9c3bdf9df7dc973686f5105c04140b36 ""
"q2f_fig.png" 1614654314 34695 af1d8fa7a33b7f04767332fb391a90f6 ""
(generated) (generated)
"doc.aux"
"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf"
"doc.pdf"
"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.log"
"doc.pdf"
"doc.log" "doc.log"
"d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/doc.pdf"
"doc.aux"

21
PS2/doc.fls
View File

@ -495,19 +495,14 @@ 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\q1a_1and50.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_1and50.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_1and50.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_1and50.png
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmr9.tfm INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmr9.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmmi9.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmsy9.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\cmextra\cmex9.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\cmextra\cmex7.tfm INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\cmextra\cmex7.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam10.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam5.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm10.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm5.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\cmextra\cmex7.tfm INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\cmextra\cmex7.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam10.tfm INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam10.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam7.tfm INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam7.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam5.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm10.tfm INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm10.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm7.tfm INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm7.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm5.tfm
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_eigenvals.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_eigenvals.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_eigenvals.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_eigenvals.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_eigenvals.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1a_eigenvals.png
@ -529,6 +524,11 @@ 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_fig1.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1civ_fig1.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1civ_fig1.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1civ_fig1.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1civ_fig1.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q1civ_fig1.png
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmmi9.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\cm\cmsy9.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\cmextra\cmex9.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msam10.tfm
INPUT C:\Users\speed\AppData\Local\Programs\MiKTeX\fonts\tfm\public\amsfonts\symbols\msbm10.tfm
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\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
@ -571,6 +571,13 @@ 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\q2c_fig2_2s.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2c_fig2_2s.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2c_fig2_2s.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2c_fig2_2s.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2c_fig2_2s.png INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2c_fig2_2s.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2f_fig.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2f_fig.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2f_fig.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2f_fig.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2f_fig.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2f_fig.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\q2f_fig.png
INPUT d:\Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux 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
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

49
PS2/doc.log
View File

@ -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 19:47 This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 21.1) (preloaded format=pdflatex 2021.2.6) 1 MAR 2021 20:20
entering extended mode 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
(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
@ -333,62 +333,67 @@ File: q1a_eigenvals.png Graphic file (type png)
Package pdftex.def Info: q1a_eigenvals.png used on input line 163. Package pdftex.def Info: q1a_eigenvals.png used on input line 163.
(pdftex.def) Requested size: 202.3529pt x 151.76526pt. (pdftex.def) Requested size: 202.3529pt x 151.76526pt.
[3 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1a_1and50.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1a_eigenvals.png (PNG copy)>] [3 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1a_1and50.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1a_eigenvals.png (PNG copy)>]
<q1cii.png, id=28, 421.575pt x 316.18124pt> <q1cii.png, id=27, 421.575pt x 316.18124pt>
File: q1cii.png Graphic file (type png) File: q1cii.png Graphic file (type png)
<use q1cii.png> <use q1cii.png>
Package pdftex.def Info: q1cii.png used on input line 276. Package pdftex.def Info: q1cii.png used on input line 278.
(pdftex.def) Requested size: 505.89pt x 379.42523pt. (pdftex.def) Requested size: 505.89pt x 379.42523pt.
[4] [4]
<q1civ_fig1.png, id=33, 421.575pt x 316.18124pt> <q1civ_fig1.png, id=32, 421.575pt x 316.18124pt>
File: q1civ_fig1.png Graphic file (type png) File: q1civ_fig1.png Graphic file (type png)
<use q1civ_fig1.png> <use q1civ_fig1.png>
Package pdftex.def Info: q1civ_fig1.png used on input line 304. Package pdftex.def Info: q1civ_fig1.png used on input line 306.
(pdftex.def) Requested size: 252.94499pt x 189.7102pt. (pdftex.def) Requested size: 252.94499pt x 189.7102pt.
<q1civ_fig2.png, id=34, 421.575pt x 316.18124pt> <q1civ_fig2.png, id=33, 421.575pt x 316.18124pt>
File: q1civ_fig2.png Graphic file (type png) File: q1civ_fig2.png Graphic file (type png)
<use q1civ_fig2.png> <use q1civ_fig2.png>
Package pdftex.def Info: q1civ_fig2.png used on input line 309. Package pdftex.def Info: q1civ_fig2.png used on input line 311.
(pdftex.def) Requested size: 252.94499pt x 189.7102pt. (pdftex.def) Requested size: 252.94499pt x 189.7102pt.
[5 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1cii.png (PNG copy)>] [5 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1cii.png (PNG copy)>]
<q1di_fig1.png, id=39, 421.575pt x 316.18124pt> <q1di_fig1.png, id=38, 421.575pt x 316.18124pt>
File: q1di_fig1.png Graphic file (type png) File: q1di_fig1.png Graphic file (type png)
<use q1di_fig1.png> <use q1di_fig1.png>
Package pdftex.def Info: q1di_fig1.png used on input line 338. Package pdftex.def Info: q1di_fig1.png used on input line 340.
(pdftex.def) Requested size: 252.94499pt x 189.7102pt. (pdftex.def) Requested size: 252.94499pt x 189.7102pt.
<q1di_fig2.png, id=40, 421.575pt x 316.18124pt> <q1di_fig2.png, id=39, 421.575pt x 316.18124pt>
File: q1di_fig2.png Graphic file (type png) File: q1di_fig2.png Graphic file (type png)
<use q1di_fig2.png> <use q1di_fig2.png>
Package pdftex.def Info: q1di_fig2.png used on input line 343. Package pdftex.def Info: q1di_fig2.png used on input line 345.
(pdftex.def) Requested size: 252.94499pt x 189.7102pt. (pdftex.def) Requested size: 252.94499pt x 189.7102pt.
<q1div.jpg, id=41, 4047.12pt x 3035.34pt> <q1div.jpg, id=40, 4047.12pt x 3035.34pt>
File: q1div.jpg Graphic file (type jpg) File: q1div.jpg Graphic file (type jpg)
<use q1div.jpg> <use q1div.jpg>
Package pdftex.def Info: q1div.jpg used on input line 358. Package pdftex.def Info: q1div.jpg used on input line 360.
(pdftex.def) Requested size: 505.89pt x 379.41656pt. (pdftex.def) Requested size: 505.89pt x 379.41656pt.
[6 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1civ_fig1.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1civ_fig2.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1di_fig1.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1di_fig2.png (PNG copy)>] [7 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1div.jpg>] [8] [6 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1civ_fig1.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1civ_fig2.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1di_fig1.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1di_fig2.png (PNG copy)>] [7 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q1div.jpg>] [8]
<q2c_fig1_1s.png, id=54, 421.575pt x 316.18124pt> <q2c_fig1_1s.png, id=54, 421.575pt x 316.18124pt>
File: q2c_fig1_1s.png Graphic file (type png) File: q2c_fig1_1s.png Graphic file (type png)
<use q2c_fig1_1s.png> <use q2c_fig1_1s.png>
Package pdftex.def Info: q2c_fig1_1s.png used on input line 458. Package pdftex.def Info: q2c_fig1_1s.png used on input line 460.
(pdftex.def) Requested size: 252.94499pt x 189.7102pt. (pdftex.def) Requested size: 252.94499pt x 189.7102pt.
<q2c_fig2_2s.png, id=55, 421.575pt x 316.18124pt> <q2c_fig2_2s.png, id=55, 421.575pt x 316.18124pt>
File: q2c_fig2_2s.png Graphic file (type png) File: q2c_fig2_2s.png Graphic file (type png)
<use q2c_fig2_2s.png> <use q2c_fig2_2s.png>
Package pdftex.def Info: q2c_fig2_2s.png used on input line 463. Package pdftex.def Info: q2c_fig2_2s.png used on input line 465.
(pdftex.def) Requested size: 252.94499pt x 189.7102pt. (pdftex.def) Requested size: 252.94499pt x 189.7102pt.
[9 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q2c_fig1_1s.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q2c_fig2_2s.png (PNG copy)>] [10] [11] [12] (d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.aux) ) <q2f_fig.png, id=56, 421.575pt x 316.18124pt>
File: q2f_fig.png Graphic file (type png)
<use q2f_fig.png>
Package pdftex.def Info: q2f_fig.png used on input line 480.
(pdftex.def) Requested size: 505.89pt x 379.42523pt.
[9 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q2c_fig1_1s.png (PNG copy)> <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q2c_fig2_2s.png (PNG copy)>] [10 <d:/Users/Speedee/Documents/University/Year5/Winter/ECE456/ProblemSets/Git/ECE_456/PS2/q2f_fig.png (PNG copy)>] [11] [12] (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: Here is how much of TeX's memory you used:
8398 strings out of 479618 8404 strings out of 479618
126163 string characters out of 2865027 126248 string characters out of 2865027
981750 words of memory out of 3000000 981750 words of memory out of 3000000
25454 multiletter control sequences out of 15000+200000 25459 multiletter control sequences out of 15000+200000
412866 words of font info for 64 fonts, out of 3000000 for 9000 412866 words of font info for 64 fonts, out of 3000000 for 9000
1141 hyphenation exceptions out of 8191 1141 hyphenation exceptions out of 8191
68i,12n,75p,1278b,2408s stack positions out of 5000i,500n,10000p,200000b,50000s 68i,12n,75p,1278b,2408s stack positions out of 5000i,500n,10000p,200000b,50000s
<C:\Users\speed\AppData\Local\MiKTeX\fonts/pk/ljfour/jknappen/ec/dpi600\tcrm1000.pk><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/cmex10.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/cmmi5.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi9.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><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr5.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr9.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/latxfont/line10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/symbols/msbm10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/symbols/msbm7.pfb> <C:\Users\speed\AppData\Local\MiKTeX\fonts/pk/ljfour/jknappen/ec/dpi600\tcrm1000.pk><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/cmex10.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/cmmi5.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmmi9.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><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr5.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmr9.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy7.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/latxfont/line10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/symbols/msbm10.pfb><C:/Users/speed/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/symbols/msbm7.pfb>
Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (12 pages, 3676324 bytes). Output written on d:/Users\Speedee\Documents\University\Year5\Winter\ECE456\ProblemSets\Git\ECE_456\PS2\doc.pdf (12 pages, 3711631 bytes).
PDF statistics: PDF statistics:
129 PDF objects out of 1000 (max. 8388607) 130 PDF objects out of 1000 (max. 8388607)
0 named destinations out of 1000 (max. 500000) 0 named destinations out of 1000 (max. 500000)
51 words of extra memory for PDF output out of 10000 (max. 10000000) 56 words of extra memory for PDF output out of 10000 (max. 10000000)

BIN
PS2/doc.pdf
View File

Binary file not shown.

BIN
PS2/doc.synctex.gz
View File

Binary file not shown.

74
PS2/doc.tex
View File

@ -155,7 +155,7 @@ legend({'Numerical','Analytical'},'Location','northwest');
\begin{subfigure}{0.4\linewidth} \begin{subfigure}{0.4\linewidth}
\centering \centering
\includegraphics[width=\textwidth]{q1a_1and50.png} \includegraphics[width=\textwidth]{q1a_1and50.png}
\caption{Probability densities for \(n=1\)\\and \(n=50\).} \caption{}
\label{fig:q3_ne} \label{fig:q3_ne}
\end{subfigure}% \end{subfigure}%
\begin{subfigure}{0.4\linewidth} \begin{subfigure}{0.4\linewidth}
@ -164,6 +164,8 @@ legend({'Numerical','Analytical'},'Location','northwest');
\caption{Comparison of first 101 numerical and analytic eigenvalues.} \caption{Comparison of first 101 numerical and analytic eigenvalues.}
\label{fig:q3_current} \label{fig:q3_current}
\end{subfigure} \end{subfigure}
\caption{(a) Probability densities for \(n=1\) and \(n=50\).
(b) Comparison of first 101 numerical and analytic eigenvalues.}
\end{figure} \end{figure}
\item %1b \item %1b
\begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)] \begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)]
@ -185,7 +187,7 @@ legend({'Numerical','Analytical'},'Location','northwest');
We use the following identity: We use the following identity:
\begin{equation} \begin{equation}
\int\sin^2{(\alpha x)}\:dx = \frac{1}{2} x -\frac{1}{4\alpha}\sin{(2\alpha x)}. \int\sin^2{(a x)}\:dx = \frac{1}{2} x -\frac{1}{4a}\sin{(2a x)}.
\label{eq:integral_ident} \label{eq:integral_ident}
\end{equation} \end{equation}
@ -247,25 +249,25 @@ legend({'Numerical','Analytical'},'Location','northwest');
\item %1ci \item %1ci
% TODO check that B is expressed correctly in all these equations (alpha, not ell, wait for pdf gen) % TODO check that B is expressed correctly in all these equations (alpha, not ell, wait for pdf gen)
From the base form of $\phi _\ell = Bsin \left( \frac {n \pi}{L} \alpha \ell \right)$, we can see that From the base form of $\phi _\ell = Bsin \left( \frac {n \pi}{L} a \ell \right)$, we can see that
$\phi _ {\ell + 1}$ and $\phi _ {\ell - 1}$ correspond to the trigonometric identities $\phi _ {\ell + 1}$ and $\phi _ {\ell - 1}$ correspond to the trigonometric identities
$sin(\alpha + B) = sin(\alpha)cos(B) + cos(\alpha)sin(B)$ and $sin(a + B) = sin(a)cos(B) + cos(a)sin(B)$ and
$sin(\alpha + B) = sin(\alpha)cos(B) + cos(\alpha)sin(B)$, respectively, where $sin(a + B) = sin(a)cos(B) + cos(a)sin(B)$, respectively, where
$\alpha = \frac{n \pi \alpha \ell}{L}$ and $B = \frac{n \pi \alpha}{L}$. $a = \frac{n \pi a \ell}{L}$ and $B = \frac{n \pi a}{L}$.
Plugging these identities into equation (7) from the assignment and simplifying, we get to this equation: Plugging these identities into equation (7) from the assignment and simplifying, we get to this equation:
\begin{equation*} \begin{equation*}
-t_0 B sin \left( \frac{n \pi \alpha \ell}{L} \right) + 2 t_0 \phi _{\ell} - t_0 sin \left( \frac{n \pi \alpha \ell}{L} \right) -t_0 B sin \left( \frac{n \pi a \ell}{L} \right) + 2 t_0 \phi _{\ell} - t_0 sin \left( \frac{n \pi a \ell}{L} \right)
\end{equation*} \end{equation*}
At this point, we notice that $\phi _ \ell = B sin \left( \frac {n \pi}{L} \alpha \ell \right)$, At this point, we notice that $\phi _ \ell = B sin \left( \frac {n \pi}{L} a \ell \right)$,
so we can factor it out. so we can factor it out.
With some minor rearranging, this leaves us with the final expression for $E$: With some minor rearranging, this leaves us with the final expression for $E$:
\begin{equation} \begin{equation}
E = 2t_0 \left( 1 - cos \left( \frac{n \pi \alpha}{L} \right) \right) E = 2t_0 \left( 1 - cos \left( \frac{n \pi a}{L} \right) \right)
\label{eq:numerical_E} \label{eq:numerical_E}
\end{equation} \end{equation}
@ -286,7 +288,7 @@ legend({'Numerical','Analytical'},'Location','northwest');
on equation (\ref{eq:numerical_E}), we get the following expression on equation (\ref{eq:numerical_E}), we get the following expression
\begin{equation*} \begin{equation*}
E = 2 t_0 \left( \frac{n^2 \pi^2 \alpha^2}{2 L^2} \right) E = 2 t_0 \left( \frac{n^2 \pi^2 a^2}{2 L^2} \right)
\end{equation*} \end{equation*}
Fully substituting the known value of $t_0$, and we can get our final expression for $E$: Fully substituting the known value of $t_0$, and we can get our final expression for $E$:
@ -388,7 +390,7 @@ H(N, 1) = -t0;
\end{equation*} \end{equation*}
\item %2b \item %2b
Homogenous boundary conditions imply that the corner entries of \(\hat{H}\) will be 0. Homogenous boundary conditions imply that the corner entries of \(\hat{H}\) will be 0.
\item %1c \item %2c
Code: Code:
\begin{lstlisting} \begin{lstlisting}
clear all; clear all;
@ -464,12 +466,22 @@ axis([0 1e-9 0 0.04]);
\caption{2s probability density.} \caption{2s probability density.}
\end{subfigure} \end{subfigure}
\end{figure} \end{figure}
\item %1d \item %2d
For the 1s level, \(E = -13.4978\) eV. For the 1s level, \(E = -13.4978\) eV.
\item %1e \item %2e
\lipsum[1]
\item %1f
\lipsum[1] \lipsum[1]
\item %2f
In the figure below we can see that the numerical and analytical results agree up to scaling by \(a\). The scale difference is expected,
as discussed in Problem 1. From (d), we also expect agreement in the curve shapes because the numerical and analytical energies for the 1s
level are very similiar. We can see that the peak value of the analytic result is very slightly higher than that of the numerical result,
which corresponds to the analytical result for the energy being slightly greater in magnitude (\(-13.6\) eV versus \(-13.4978\) eV).
\begin{figure}[H]
\centering
\includegraphics[width=\textwidth]{q2f_fig.png}
\caption{Numerical result (black line) and analytical solution scaled by \(a\) (orange circles).}
\end{figure}
\end{enumerate} \end{enumerate}
@ -477,28 +489,28 @@ axis([0 1e-9 0 0.04]);
\begin{enumerate}[align=left,leftmargin=*,labelsep=1em,label=\bfseries(\alph*)] \begin{enumerate}[align=left,leftmargin=*,labelsep=1em,label=\bfseries(\alph*)]
\item %2a \item %3a
\lipsum[1] \lipsum[1]
\item %2b \item %3b
\begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)] \begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)]
\item %1di \item %3bi
\lipsum[1] \lipsum[1]
\item %1dii \item %3bii
\lipsum[1] \lipsum[1]
\item %1diii \item %3biii
\lipsum[1] \lipsum[1]
\item %1div \item %3biv
\lipsum[1] \lipsum[1]
\item %1dv \item %3bv
\lipsum[1] \lipsum[1]
\item %1dvi \item %3bvi
\lipsum[1] \lipsum[1]
\item %1dvii \item %3bvii
\lipsum[1] \lipsum[1]
\end{enumerate} \end{enumerate}
\item %1c \item %3c
\lipsum[1] \lipsum[1]
\item %1d \item %3d
\lipsum[1] \lipsum[1]
\end{enumerate} \end{enumerate}
@ -507,15 +519,15 @@ axis([0 1e-9 0 0.04]);
\begin{enumerate}[align=left,leftmargin=*,labelsep=1em,label=\bfseries(\alph*)] \begin{enumerate}[align=left,leftmargin=*,labelsep=1em,label=\bfseries(\alph*)]
\item %2a \item %4a
\lipsum[1] \lipsum[1]
\item %2b \item %4b
\begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)] \begin{enumerate}[align=left,leftmargin=*,labelsep=0em,label=(\roman*)]
\item %1di \item %4bi
\lipsum[1] \lipsum[1]
\item %1dii \item %4bii
\lipsum[1] \lipsum[1]
\item %1diii \item %4biii
\lipsum[1] \lipsum[1]
\end{enumerate} \end{enumerate}

BIN
PS2/q2f_fig.png
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 30 KiB

After

Width:  |  Height:  |  Size: 34 KiB