Paper VII: Quantum Seed Calculus

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \path[draw,line width=.8pt] (2.8,2.45) circle (1.62);
4 \draw[black!35] (2.8,2.45) ellipse (1.62 and .45);
5 \draw[black!35] (2.8,2.45) ellipse (.6 and 1.62);
6 \draw[dashed,black!65] (2.8,3.25) ellipse (1.4 and .31);
7 \draw[->] (2.8,2.45) -- (2.8,4.08);
8 \node[font=\small,align=center,font=\scriptsize] at (2.8,0.2) {Cap flux at $\theta=\pi/3$ is $\pi/2$.};
9 \draw[black!13,line width=.25pt] (6.4,0.85) -- (6.4,3.65);
10 \draw[] (6.4,0.79) -- (6.4,0.91);
11 \node[font=\small,align=center,font=\scriptsize] at (6.4,0.59) {0};
12 \draw[black!13,line width=.25pt] (6.4,0.85) -- (13.1,0.85);
13 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (6.24,0.85) {0};
14 \draw[black!13,line width=.25pt] (6.4,2.016667) -- (13.1,2.016667);
15 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (6.24,2.016667) {0.25};
16 \draw[black!13,line width=.25pt] (6.4,3.183333) -- (13.1,3.183333);
17 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (6.24,3.183333) {0.5};
18 \draw[->,line width=.6pt] (6.4,0.85) -- (13.22,0.85);
19 \draw[->,line width=.6pt] (6.4,0.85) -- (6.4,3.77);
20 \node[font=\small,align=center,font=\scriptsize] at (9.75,0.3) {polar angle $\theta$};
21 \node[font=\small,align=center,anchor=west,font=\scriptsize] at (6.4,4.05) {$F_{\theta\phi}=\frac12\sin\theta$};
22 \draw[line width=1.1pt] plot coordinates {(6.4,0.85) (6.467,0.923292) (6.534,0.996511) (6.601,1.069586) (6.668,1.142444) (6.735,1.215014) (6.802,1.287223) (6.869,1.359001) (6.936,1.430276) (7.003,1.500979) (7.07,1.57104) (7.137,1.640388) (7.204,1.708957) (7.271,1.776678) (7.338,1.843485) (7.405,1.909311) (7.472,1.974092) (7.539,2.037763) (7.606,2.100263) (7.673,2.161528) (7.74,2.221499) (7.807,2.280116) (7.874,2.337323) (7.941,2.393061) (8.008,2.447277) (8.075,2.499916) (8.142,2.550927) (8.209,2.600259) (8.276,2.647864) (8.343,2.693695) (8.41,2.737706) (8.477,2.779855) (8.544,2.820098) (8.611,2.858398) (8.678,2.894716) (8.745,2.929015) (8.812,2.961263) (8.879,2.991427) (8.946,3.019478) (9.013,3.045388) (9.08,3.069132) (9.147,3.090685) (9.214,3.110027) (9.281,3.127139) (9.348,3.142004) (9.415,3.154606) (9.482,3.164934) (9.549,3.172978) (9.616,3.178729) (9.683,3.182182) (9.75,3.183333) (9.817,3.182182) (9.884,3.178729) (9.951,3.172978) (10.018,3.164934) (10.085,3.154606) (10.152,3.142004) (10.219,3.127139) (10.286,3.110027) (10.353,3.090685) (10.42,3.069132) (10.487,3.045388) (10.554,3.019478) (10.621,2.991427) (10.688,2.961263) (10.755,2.929015) (10.822,2.894716) (10.889,2.858398) (10.956,2.820098) (11.023,2.779855) (11.09,2.737706) (11.157,2.693695) (11.224,2.647864) (11.291,2.600259) (11.358,2.550927) (11.425,2.499916) (11.492,2.447277) (11.559,2.393061) (11.626,2.337323) (11.693,2.280116) (11.76,2.221499) (11.827,2.161528) (11.894,2.100263) (11.961,2.037763) (12.028,1.974092) (12.095,1.909311) (12.162,1.843485) (12.229,1.776678) (12.296,1.708957) (12.363,1.640388) (12.43,1.57104) (12.497,1.500979) (12.564,1.430276) (12.631,1.359001) (12.698,1.287223) (12.765,1.215014) (12.832,1.142444) (12.899,1.069586) (12.966,0.996511) (13.033,0.923292) (13.1,0.85)};
23 \node[font=\small,align=center,font=\scriptsize] at (13.1,0.58) {$\pi$};
24 \node[font=\small,align=center,font=\scriptsize] at (9.7,4.45) {The density vanishes at coordinate poles.};
25 \end{tikzpicture}

Back to source controls

Back to Paper VII: Quantum Seed Calculus