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Homework Help: Determining Neutron Wavelength with mass alone

  1. Sep 26, 2011 #1
    1. The problem statement, all variables and given/known data

    Consider a particle of mass m in the potential

    V(z)=mgz z>0, infinity if z<0

    Show that the wavelength of a neutron (m~1000MeV/c^2) is on the order of 10um.

    2. Relevant equations

    p=(2m(E-mgz))1/2
    [itex]\lambda[/itex]=h/p

    3. The attempt at a solution

    The most direct solution would seem to simply be

    h/(2m(E-mgz))1/2 (with appropriate substitutions)

    however, that still leaves the factors of g and z to be resolved... I could take z as 1, but there's still g with a units problem (m/s/s vs MeV and MeV/c^2).

    Any suggestions?
     
  2. jcsd
  3. Sep 27, 2011 #2

    vela

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    Try drawing a diagram of the potential and then sketch what the ground-state wave function will look like. That should give you an idea for a relationship between the wavelength and the energy of the neutron.
     
  4. Sep 27, 2011 #3
    So, for z>0 the potential will increase linearly (holding m and g constant).
     
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