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Minimum Uncertainty in Electron Position: Rectangular Wave in k-space

  1. Nov 4, 2012 #1
    1. The problem statement, all variables and given/known data
    In the case of an electron wave packet, the function A(k) has a rectangular shape, i.e. it is equal to A0 if k0-a<k<k0+a, and zero everywhere else. (a) Find the minimal uncertainty of electron position. (b) Find the electron wavefunction.


    2. Relevant equations
    ΔxΔp=h/4pi (for min uncertainty)
    ΔxΔκ=1/4pi
    ψ=Asin2pi(κx-vt)

    3. The attempt at a solution
    a) κ=1/λ
    ΔxΔκ=ΔxΔ(1/λ)=1/4pi
    Δx=1/(4pi(Δ(1/λ))= 1/(4pi(Δ(k/2pi))
    Because k0+a -(k0-a)=2a, the span of k is 2a?
    Δx=2pi/(4pi*2a)=1/2a
    I am not sure if I am doing this correctly. My lecture notes talk about k and λ space, making no mention of κ, but my book uses equations with kappa. It seems like κ=k/2pi, but maybe I have that wrong.

    b)ψ=Asin2pi(κx-vt) Not sure where to go from here

    I appreciate any help I can get!
     
  2. jcsd
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