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Dispersion in for a free particle

  1. Sep 29, 2011 #1
    Hey,
    I am trying to calculate the dispersions [itex]\Delta[/itex]P and [itex]\Delta[/itex]X for a free particle with definite momentum [itex]\Phi[/itex](x) = Aexp(ikx) where A is a normalization constant. This i get
    [itex]\Delta[/itex]P = 0
    [itex]\Delta[/itex]X = [itex]\infty[/itex]
    What physical interpretation can I give to these results? Is is that the momentum is well specified and can always be obtained with certainty and that the position can be anywhere?
    Also,
    I am trying to solve the same problem for a free particle in the state
    [itex]\Phi[/itex](x) = A*Cos(kx).
    I get integrals involving sin and cos to be evaluated at [itex]\infty[/itex]. Using taylor expansion, i argue that
    [itex]\Delta[/itex]P = [itex]\infty[/itex]
    [itex]\Delta[/itex]X = [itex]\infty[/itex]

    Am I correct?
    The function [itex]\Phi[/itex](x) = A*Cos(kx) seems not to be normalizable to me, so should not be used to represent the state of a quantum mechanical system. What do you think?

    Thanks

    Marcel
     
  2. jcsd
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