Time-Dependent Perturbation Theory and Fermi's Golden Rule · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

How fast one state becomes another

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

  1. Name the two ingredients of the golden rule.

    • Temperature and pressure
    • Matrix element and density of final states
    • Mass and charge

  2. What does a time-switched perturbation drive?

    • Transitions between states
    • New conservation laws
    • A frozen, changeless system

  3. Absorption, emission, and decay rates come from the golden rule.

    Circle one:   True   False

  4. A perturbation acts for a finite time. What do you compute to first order?

    • The transition amplitude over that window
    • The exact eternal future
    • Nothing until infinite time

  5. Two decays share a matrix element but one offers more final states. Which is faster?

    • The one with fewer final states
    • Both run at the same speed
    • The one with more final states

  6. In a decay problem, what plays the density of states?

    • How hot the laboratory is
    • How many final states sit at the right energy
    • How many atoms you started with

  7. A classmate computes a rate with zero available final states and gets a nonzero answer. What is wrong?

    • With no landing places the rate must vanish, so the density was mishandled
    • Zero states always give fast rates
    • The matrix element was too small

  8. An excited atom decays faster in one setup than another, matrix element unchanged. Explain.

    • The atom forgot its energy
    • Time runs faster in that setup
    • That setup offers more final states to land in
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Answer key

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

How fast one state becomes another W1-mt_zDSASGF7SC-s1

  1. Matrix element and density of final states · Link strength plus landing-place count.
  2. Transitions between states · Switching on in time moves the system across states.
  3. True · All three are golden-rule rates.
  4. The transition amplitude over that window · Finite window, first-order amplitude.
  5. The one with more final states · Count landing places first.
  6. How many final states sit at the right energy · Density means available landings at the right energy.
  7. With no landing places the rate must vanish, so the density was mishandled · No landings, no decay.
  8. That setup offers more final states to land in · Same link, more landings, faster decay.
Worksheet · LightMySky