Identical Particles and the Symmetry of a Many-Body State · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

When swapping changes nothing

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

  1. How do you build a symmetric two-particle state?

    • Take the difference of swapped products
    • Take a single product with no partner
    • Take the sum of swapped products

  2. You swap two identical particles. What stays the same?

    • Every prediction stays the same
    • The wave always flips sign
    • The particles gain tracking labels

  3. What does swapping do to an antisymmetric state?

    • Nothing at all
    • It flips the sign
    • It doubles the amplitude

  4. How does antisymmetry forbid two fermions sharing one state?

    • The Born rule deletes the extra particle
    • Photons occupy the slots first
    • Same-state subtraction cancels to zero

  5. Why can lasers pack huge photon numbers into one beam?

    • Mirrors force the photons together
    • Bosons use symmetric states that allow sharing
    • Exclusion squeezes them into one slot

  6. Why do electrons stack into separate atomic shells?

    • Electrons must each take a different state
    • Electrons are bosons
    • Shells attract electrons pairwise

  7. Two electrons can occupy one exact same state at the same place.

    Circle one:   True   False

  8. Why do singlet and triplet helium levels split in energy?

    • Different photon counts in the beam
    • Different Born probabilities
    • Different electric repulsion of the two spatial layouts
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Answer key

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

When swapping changes nothing W1-mt_hns-eEGeHU-s1

  1. Take the sum of swapped products · Adding makes the swap change nothing.
  2. Every prediction stays the same · Indistinguishability means no measurement can tell.
  3. It flips the sign · Antisymmetric means the swap trades plus for minus.
  4. Same-state subtraction cancels to zero · The difference of identical terms vanishes, so the state cannot exist.
  5. Bosons use symmetric states that allow sharing · Symmetric states permit unlimited sharing of one mode.
  6. Electrons must each take a different state · Exclusion forbids sharing, so electrons fill upward.
  7. False · Antisymmetry cancels that shared state to zero.
  8. Different electric repulsion of the two spatial layouts · Symmetric and antisymmetric layouts feel different repulsion.
Worksheet · LightMySky