Atomic01 - University of Cape Town

PHY322S Atomic Physics .
Heisenberg microscope (cont.)
Photons transfer momentum to the particle from which they scatter.
Magnitude of p is same before and after collision.
Uncertainty of photon y-momentum equal to uncertainty in particle y-
momentum
−p sin(θ/2) ≤ p y ≤ p sin(θ/2)
Small angle approximation: ∆p y = 2p sin(θ/2) ≃ pθ
de Brogile gives p = h/λ so ∆p y ≃ hθ/λ
and ∆y ≥ λ/θ hence
∆p y ∆y ≃ h
This is the Heisenberg uncertainty principle.
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