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Wavefunction and degree of localization

  1. Aug 1, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose that there is a wavefunction [itex]\Psi (x,0)[/itex] where 0 is referring to [itex]t[/itex]. Let us also say that [itex]a(k) = (C\alpha/\sqrt \pi )exp(-\alpha^2k^2)[/itex] is the spectral contents (spectral amplitudes) where [itex]k[/itex] is defined as wavenumber [itex]k[/itex]. [itex]\alpha[/itex] and [itex]C[/itex] is some constant

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

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

    Thanks.


    2. Relevant equations
    Fourier transform.


    3. The attempt at a solution
     
  2. jcsd
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