Another important uncertainty principle is encountered in time-dependent systems. It relates the lifetime of a state t
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Another important uncertainty principle is encountered in time-dependent systems. It relates the lifetime of a state Δt with the measured spread in the photon energy ΔE associated with the decay of this state to a stationary state of the system. “Derive” the relation ΔE Δt ≥ h/2 in the following steps
a. Starting from E = p2x/2m and ∆E = (dE/dpx) Δpx show that ΔE = vx Δpx.
b. Using vx = Δx/Δt, show that ΔE Δt = ΔpxΔx ≥ h/2.
c. Estimate the width of a spectral line originating from the decay of a state of lifetime 1.0 × 10−9 s and 1.0 × 10−11 s in inverse seconds and inverse centimeters.
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