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QM: Probability of measuring momentum

  1. Dec 22, 2017 #1
    Hi all,

    My question is in reference to the following paper: https://arxiv.org/pdf/1202.1783.pdf

    In equation 3.8, the author computes an order-of-magnitude approximation of probability of measuring negative momentum from the following wavefunction:
    $$
    \Psi_k =\sum_{k=1,2} \frac{B_k}{\sqrt{4\sigma ^2 + 2it}} \exp (ip_k (x - \frac{p_k}{2}t) - \frac{(x - p_k t)^2}{4\sigma ^2 + 2it})
    $$

    Equation 3.8 is:
    $$\int_{-\infty}^{0} dp \exp[-200(p-0.3)^2]$$

    From what I understand, one should first take a Fourier-Transform of the above wavefuction, find ##|\Psi_k (p,t)|^2## and then take an integral from ##-\infty## to ##0## to get an expression that allows such a computation.

    However, I'm not so sure what the term "order-of-magnitude approximation" entails. Would it be right to assume that the computation steps I mentioned above only considers terms of the highest order of magnitude?

    Thanks in advance for any assistance.
     
    Last edited by a moderator: Dec 22, 2017
  2. jcsd
  3. Dec 24, 2017 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    The article you cite says eq 3.8 is for the particular case

    and:

    The article integrates a gaussian centered at p1 over negative values of p. Does that make sense as computation for Prob( p < 0) if we ignore the component of the wave that involves p2?
     
  4. Dec 26, 2017 #3
    Thanks for your response.

    I suppose not, since we are leaving out an entire part of the wavefunction in our computation. However the authors state that this was an order-of-magnitude estimate. Is this a valid line of reasoning?
     
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