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Total Reflection of a Classical Particle off a Two-Dimensional Potential

  1. Jun 11, 2012 #1
    1. The problem statement, all variables and given/known data
    This question is motivated by Problem 8, Ch 1 of Cohen-Tannoudji's "Quantum Mechanics". Suppose that you are given a two dimensional potential of the form V(x,y) = V if x>0 and V(x,y)=0 if x<0. A particle travels toward the the potential obliquely, i.e. neither parallel to the x-axis nor to the y-axis, and its kinetic energy is less than V. Describe the classical trajectory of the particle upon reflection.

    2. Relevant equations

    Presumably, conservation of the y-component of momentum and conservation of energy.

    3. The attempt at a solution
    The classical trajectory is described as a "lateral shift upon reflection." I assume that the answer will somehow depend on the angle \theta between the trajectory and the normal to the surface. Thanks!
    Last edited: Jun 11, 2012
  2. jcsd
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