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Schrodinger Equation: Particle in a Box

  1. Oct 11, 2011 #1

    jgens

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    1. The problem statement, all variables and given/known data

    We have been examining a one-dimensional infinite square well where the infinite walls are located at -b and +b. The energy levels in this quantum system are non-degenerate, that is for each energy there is only one wave function. Let us place an infinite potential step between -b/2 and +b/2.
    • Is the particle more likely to be in the left or the right infinite square well?
    • What are the new energy levels and wave functions of this modified system?
    • Are the energy levels degenerate, and if so, what is the degeneracy?
    • Are the new energies higher or lower than the box without the infinite step?

    2. Relevant equations

    Time-independent Schrodinger Equation

    3. The attempt at a solution

    My main question involves how to interpret this problem. In my reading, the potential is just V(x) = 0 for -b < x < a and V(x) = +infinity for a < x < b where -b/2 < a < b/2. If my reading is correct, then wouldn't the particle only be in the left square well? (Since any particle would just be reflected from the region with infinite potential)

    Thanks
     
  2. jcsd
  3. Oct 12, 2011 #2
    I read it the same way, all the step does is to reduce the width of the well.
     
  4. Oct 12, 2011 #3

    vela

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    I read it to mean that V(x)=0 for -b≤x≤-b/2 or b/2≤x≤b and V(x)=infinity everywhere else.
     
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