A beam of protons travelling with a constant speed u parallel to the X axis, occ

Question

A beam of protons travelling with a constant speed u parallel to the X axis, occupies the entire half-space to the left of the YZ plane at t=0. At this time it strikes the YZ plane, which is opaque to protons except for a small rectangular opening of size (2mm x 1mm) centered on the origin with its longer side parallel to the Y axis. After the beam passes through the opening to the right of the YZ plane, what are the uncertainties ?vy and ?vz in the y and the z components of velocity of a proton in the beam? What were the values of ?vy and ?vz before the beam passed through the opening? A beam of protons travelling with a constant speed u parallel to the X axis, occupies the entire half-space to the left of the YZ plane at t=0. At this time it strikes the YZ plane, which is opaque to protons except for a small rectangular opening of size (2mm x 1mm) centered on the origin with its longer side parallel to the Y axis. After the beam passes through the opening to the right of the YZ plane, what are the uncertainties ?vy and ?vz in the y and the z components of velocity of a proton in the beam? What were the values of ?vy and ?vz before the beam passed through the opening?

Explanation / Answer

Let d be delta (small amount) dp * dx > h Heisenberg Uncertainty Principle dv > h / (m * dx) dvx > 6.63 * 10E-34 / (1.67 * 10E-27 * .001) = 4 * 10E-4 m/s (some texts may use h-bar or h/(2*pi)) Do the same for the y component with dy = .002 The uncertainty before striking the opening is zero because both dx and dy are infinite.

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