• Figure 3. Transmitted neutron flux
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    Figure 3. Transmitted neutron flux as a function of gap height in the Laue–Langevin experiment shows a clear threshold near 15 µm and indications of steps at larger gap heights, consistent with the quantum-mechanical prediction (red curve). The blue curve is what one expects simply from the increasing phase-space acceptance of the gap. The horizontal line indicates the detector’s background level.
    The experiment’s energy resolution is not limited only by statistics. The quantum-mechanical uncertainty relation
    ΔEΔt≳ℏ����≳ℏ
    also comes into play. The 0.01 s it takes a neutron to traverse the 10-cm-long gap in this experiment limits the energy resolution of the quantum-well eigenstates to 0.07 peV. One could, of course, do a hundred thousand times better if one could keep the neutron trapped in the well for its full lifetime—about 15 minutes.

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