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Momentum Shell

physicsstatistical mechanicscetztikz

See also https://diagrams.janosh.dev/ergodic.


Momentum Shell

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  Code

  LaTeX

momentum-shell.tex (19 lines)

\documentclass[tikz]{standalone}

\begin{document}
\begin{tikzpicture}[thick]

  % Axes
  \def\x{5}\def\y{3}
  \draw[->] (-\x-0.5,0) -- (\x+0.5,0) node[right] {$q_1$};
  \draw[->] (0,-\y-0.5) -- (0,\y+0.5) node[above] {$q_2$};

  % Ellipse
  \draw[blue,fill=blue,fill opacity=0.05] (0,0) circle [x radius=\x, y radius=\y];
  \coordinate[pin={[pin distance=25,scale=0.8]85:$\sqrt{2E/m}$}] (r1) at (\x,0);
  \coordinate[pin={[pin distance=25,scale=0.8]30:$\sqrt{2E/k}$}] (r2) at (0,\y);
  \node[blue] at (10:\x-1) {$P$};

\end{tikzpicture}
\end{document}

  Typst

momentum-shell.typ (37 lines)

#import "@preview/cetz:0.3.2": canvas, draw

#set page(width: auto, height: auto, margin: 3pt)

#canvas({
  import draw: line, content, circle

  let rx = 4
  let ry = 2.2
  let arrow-style = (mark: (end: "stealth", fill: black), stroke: 1pt)

  // Axes
  line((-rx - 0.5, 0), (rx + 0.5, 0), ..arrow-style)
  content((rx + 0.5, 0), $q_1$, anchor: "west", padding: 2pt)

  line((0, -ry - 0.5), (0, ry + 0.5), ..arrow-style)
  content((0, ry + 0.5), $q_2$, anchor: "south", padding: 2pt)

  // Ellipse
  circle(
    (0, 0),
    radius: (rx, ry),
    stroke: blue,
    fill: rgb(0%, 0%, 100%, 5%),
    name: "ellipse",
  )

  // Labels for radii
  content((rx + .2, 1), $sqrt(2E \/ m)$, anchor: "south-west", padding: 1pt, name: "r1")
  line((rx, 0), "r1.south", stroke: 0.2pt)
  content((0.5, ry + .5), $sqrt(2E \/ k)$, anchor: "south-west", padding: 1pt, name: "r2")
  line((0, ry), "r2.south-west", stroke: 0.2pt)

  // Label P
  content((3, 1), text(fill: blue)[$P$])
})