Saturday, 6 August 2016

quantum mechanics - Uncertainty in the angle by using Heisenberg's uncertainty principle





Given an electron with mass 9.1×1031kg is moving along x-axis with velocity 106ms1 and passes through a screen with slit Δy=109. Is it possible to find the uncertainty of angle between the final vector and the x-axis?



My attempt:



  1. Finding the uncertainty of momentum Δp by using the Heisenberg's uncertainty principle.

  2. Solving the uncertainty of angle with the momentum along x-direction px, by using tan(Δθ)=Δpypx


I doubt step(2) because we are looking for uncertainty but not the angle itself. I have no idea about the uncertainty.



Answer



I think you are missing something.



According to Heisenberg's uncertainty principle,


ΔyΔpy


If Δvy is the uncertainty in velocity along the y- direction, then


mΔyΔvymΔyvxΔθΔθmvxΔy


where we have taken Δθ be the uncertainty in the angle between the x- and y- component of velocities.


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