The Path Integral and the Sum Over Histories · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Every path counts, one path survives

Science · Quantum & Modern Physics · ages 23-24
Name ______________________   Date ____________

  1. What do you sum over to build a propagator?

    • Only the classical trajectory
    • Every path from start to finish
    • Only paths that avoid barriers

  2. In the sum over histories, what weight does each path carry?

    • A phase set by its action
    • A vote of exactly one
    • A mass equal to its length

  3. A dark double-slit fringe is a place where the path contributions cancel.

    Circle one:   True   False

  4. Two paths reach the screen with crest meeting trough. What appears there?

    • A dark fringe, since the contributions cancel
    • A bright fringe, since all arrivals glow
    • Two separate dots side by side

  5. Why does the classical path survive the sum?

    • It is the shortest path of all
    • It carries more mass than the rest
    • Its neighbors add in step while the rest cancel

  6. How does tunnelling fit the same picture?

    • Particles borrow energy to climb over
    • Barrier-crossing paths count with shrinking weight
    • The barrier paths are deleted from the sum

  7. Gamow used this picture for alpha decay. What did the small surviving weight explain?

    • Why particles leak out with a definite half-life pattern
    • Why nuclei can never decay
    • Why every nucleus decays in one second

  8. When does the stationary-phase limit fail?

    • When the action is enormous
    • When only one path exists
    • Near turning points, barriers, or rival stationary paths
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Every path counts, one path survives W1-mt_QRLheflB1O-s1

  1. Every path from start to finish · The sum runs over all paths, including barrier crossers.
  2. A phase set by its action · Each path adds one arrow fixed by its action.
  3. True · Out-of-step arrivals wipe each other out, leaving darkness.
  4. A dark fringe, since the contributions cancel · Crest against trough cancels, which reads as dark.
  5. Its neighbors add in step while the rest cancel · Near the stationary path the arrows agree, elsewhere they cancel.
  6. Barrier-crossing paths count with shrinking weight · Crossers stay in the sum with rapidly shrinking weight.
  7. Why particles leak out with a definite half-life pattern · The leak's size sets the decay rate Gamow computed.
  8. Near turning points, barriers, or rival stationary paths · Those are the places where cancellation stops being clean.
Worksheet · LightMySky