# QM: Probability of measuring momentum

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1. Dec 22, 2017

### WWCY

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. Dec 24, 2017

### Stephen Tashi

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?

3. Dec 26, 2017