Angular Momentum Quantization

angular-momentum-quantization.typ (100 lines)

#import "@preview/cetz:0.3.4": canvas, draw
#import draw: line, content, circle, arc, on-layer

#set page(width: auto, height: auto, margin: 8pt)

// Define colors matching the TikZ diagram
#let green_color = rgb("#77d477") // Adjust green to match target
#let blue_color = rgb("#1a1aff") // Lighter blue to match target
#let red_color = rgb("#ff0000")

#canvas({
  // Constants
  let zmax = 2.5
  let l = 2
  let h = 0.85 // Spacing between quantized levels
  let R = calc.sqrt(l * (l + 1)) * h // total angular momentum radius

  // Draw coordinate system
  let arrow_style = (mark: (end: "stealth", fill: black))
  let vector_style = (mark: (end: "stealth", fill: green_color, scale: 0.8), stroke: green_color + 1.1pt)

  // Draw axes - z-axis first (to position things relative to it)
  line((0, -2.7 * h), (0, zmax), stroke: black + 1pt, ..arrow_style, name: "z-axis")
  line((0, 0), (zmax, 0), stroke: black + 1pt, ..arrow_style, name: "y-axis")
  line((0, 0), (-0.62 * zmax, -0.55 * zmax), stroke: black + 1pt, ..arrow_style, name: "x-axis")

  // Add axis labels
  content("z-axis.end", $L_z$, anchor: "west", padding: (left: 3pt), size: 13pt)
  content("y-axis.end", $L_y$, anchor: "south", padding: (bottom: 3pt), size: 13pt)
  content("x-axis.end", $L_x$, anchor: "south", padding: (bottom: 6pt, left: -9pt), size: 13pt)

  // Draw blue dashed ellipse to the left of the z-axis (matching target)
  // This needs to be fully to the left of the z-axis
  let ellipse_center_x = -R
  let ellipse_center_y = h // Position at m=1 level
  let ellipse_height = 0.55 * h

  arc(
    (ellipse_center_x, ellipse_center_y),
    radius: (R * 0.955, ellipse_height),
    start: 0deg,
    stop: 360deg,
    stroke: (dash: "dashed", paint: blue_color, thickness: 0.6pt),
    name: "ellipse-m1",
    anchor: "arc-center",
  )

  // Draw origin with charge+
  on-layer(
    1,
    content(
      (0, 0),
      text(baseline: -0.2pt)[$+$],
      size: 13pt,
      frame: "circle",
      fill: red_color,
      stroke: none,
      name: "origin",
    ),
  )


  // Draw quantized Lz levels and vectors
  for m in range(-l, l + 1) {
    // Calculate coordinates
    let y = m * h
    let rx = calc.sqrt(R * R - (m * h) * (m * h))

    // Draw blue horizontal line from z-axis to endpoint
    line((0, y), (rx, y), stroke: blue_color + 0.6pt, name: "level-" + str(m))

    // Add Lz level labels with proper formatting
    content((0, y), $#m thin ħ$, anchor: "east", padding: (right: 6pt), size: 15pt)

    // Draw green angular momentum vector
    line((0, 0), (rx, y), ..vector_style, name: "vector-" + str(m))
  }

  // Draw the green half-circle (after vectors to ensure it aligns)
  arc(
    (0, 0),
    start: 90deg,
    stop: -90deg,
    radius: R,
    stroke: green_color + .8pt,
    name: "L-circle",
    anchor: "origin",
  )

  // Add the green L label near the +1h vector
  let L_position_x = 0.95 * R
  let L_position_y = 1.45 * h // Slightly above the m=1 level

  content(
    (L_position_x, L_position_y),
    text(fill: green_color, weight: "bold", size: 19pt)[L],
    anchor: "west",
  )
})