The Wavefunction and the Born Probability Rule · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Where the particle might be

Science · Quantum & Modern Physics · ages 18-20
Name ______________________   Date ____________

  1. The square of the wave function gives the probability density.

    Circle one:   True   False

  2. What is the wave function psi?

    • Something you can see and touch directly
    • An encoding of where it might be found
    • The exact position the particle owns

  3. How do you get the chance of finding the particle in a small region?

    • Multiply the density by region size
    • Divide the region size by the density
    • Read the wave function phase alone

  4. Electrons arrive one by one and dots slowly form stripes. What does that show?

    • Single landings are chancy but follow the squared wave pattern
    • Each electron landing is predictable exactly
    • The slits steer each electron by force

  5. What must the total probability over all space equal?

    • Zero
    • The particle mass
    • One

  6. How does the wave function differ from the probability density?

    • They are exactly the same thing
    • Psi can be complex and cancel, while its square is real and never negative
    • The density is complex and psi is always real

  7. Density is tall in region A and near zero in region B. Where will repeated measurements mostly land?

    • Spread evenly across A and B
    • Mostly in A, rarely in B
    • Mostly in B, rarely in A

  8. A student says the electron travels a definite path through one slit. What is wrong?

    • Nothing, paths are always definite
    • Slits cannot affect particles at all
    • Position is returned by measurement, not owned along the way
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Answer key

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

Where the particle might be W1-mt_elzmbBzmKE-s1

  1. True · That squaring step is the Born rule turning psi into predictions.
  2. An encoding of where it might be found · Psi holds everything knowable about chances, not a visible object.
  3. Multiply the density by region size · Density times stretch gives the chance, and all stretches total to one.
  4. Single landings are chancy but follow the squared wave pattern · No single dot can be foretold, yet the crowd of dots traces the density.
  5. One · The particle must turn up somewhere, so all chances add to one.
  6. Psi can be complex and cancel, while its square is real and never negative · Interference needs cancelling psi, but chances must stay real and non negative.
  7. Mostly in A, rarely in B · Tall density collects many hits while near zero density collects almost none.
  8. Position is returned by measurement, not owned along the way · The wave spreads through both slits, and only the screen hit returns a position.
Worksheet · LightMySky