The Quantum Harmonic Oscillator and Zero-Point Energy · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The ladder with equal rungs: quantum oscillator

Science · Quantum & Modern Physics · ages 20-21
Name ______________________   Date ____________

  1. What is the lowest possible energy of a quantum oscillator with rung spacing E?

    • Zero
    • One full quantum
    • Half a quantum

  2. How are the energy levels of a quantum oscillator spaced?

    • Widening gaps like the square well
    • Equal rungs of one quantum
    • A single level only

  3. Vibrating molecular bonds are modelled as quantum oscillators.

    Circle one:   True   False

  4. Why can the oscillator not sit still at the bottom of its parabola?

    • Friction drains it to a stop
    • Pinning position spreads momentum, costing kinetic energy
    • The walls absorb the motion

  5. A spectrum shows perfectly equal gaps between levels. Which trap fits?

    • Quantum oscillator
    • Square well
    • Free particle

  6. You squeeze a bound particle into a narrower spot. What happens to its minimum energy?

    • It drops lower
    • It stays the same
    • It rises higher

  7. A bond vibrates with evenly spaced levels 0.2 eV apart. What is its ground-state energy?

    • 0 eV
    • 0.1 eV
    • 0.2 eV

  8. A student says cooling to absolute zero brings the oscillator to rest at the bottom. What is the error?

    • Zero-point motion remains: half a quantum stays
    • Absolute zero freezes all motion entirely
    • The levels collapse into one
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Answer key

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

The ladder with equal rungs: quantum oscillator W1-mt_HyDxmqyReX-s1

  1. Half a quantum · The ground state carries half a quantum, and nothing sits lower.
  2. Equal rungs of one quantum · The parabola gives a ladder with identical rungs.
  3. True · Bond nuclei wobble like masses on a spring, matching the ladder.
  4. Pinning position spreads momentum, costing kinetic energy · Tight position means wild momentum, and that spread is energy.
  5. Quantum oscillator · Equal gaps are the oscillator signature; square-well gaps widen.
  6. It rises higher · Narrower localisation means wilder momentum and higher minimum energy.
  7. 0.1 eV · Ground state is half the rung spacing: half of 0.2 eV is 0.1 eV.
  8. Zero-point motion remains: half a quantum stays · Zero-point energy never vanishes, even at absolute zero.
Worksheet · LightMySky