# Wavefunction and degree of localization

1. Aug 1, 2012

### argonsonic

1. The problem statement, all variables and given/known data
Suppose that there is a wavefunction $\Psi (x,0)$ where 0 is referring to $t$. Let us also say that $a(k) = (C\alpha/\sqrt \pi )exp(-\alpha^2k^2)$ is the spectral contents (spectral amplitudes) where $k$ is defined as wavenumber $k$. $\alpha$ and $C$ is some constant

My question is, why do we calculate $\Delta x$ by looking at where the value of $\Psi (x)$ diminish by $1/e$ from the maximum possible value of $\Psi (x)$?

Also, although the width of the $\Psi (x)$ packet is $4\alpha$, we define $\Delta x$ as $\alpha$. Why is it like this?

Thanks.

2. Relevant equations
Fourier transform.

3. The attempt at a solution

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