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Homework Help: 3-dimensional particle in a box

  1. May 8, 2008 #1

    eit32

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    If I know how to get a wave function for a 3-dimensional particle in a box problem, what adjustments must I make to solve the same problem for a particle traveling in the +z direction in a tube of infinite length?

    Box:
    0<x<a
    0<y<b
    0<z<c

    Tube:
    0<x<a
    0<y<a
    0<z<infinity
     
    eit32, May 8, 2008
  2. jcsd
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  3. May 8, 2008 #2

    lzkelley

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    Thats the basic idea. The primary effect of that, is that the wave number in the z direction won't have the same bounds.
    Most likely the wave will be a real exponential (decaying or growing) -> and clearly it can't be growing unbounded.

    Does that help? Try throwing the new boundary conditions into the differential wave equation.
     
    lzkelley, May 8, 2008
  4. May 8, 2008 #3

    eit32

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    well i think i problem i'm running into is that the wave function for the box isin the form of a sine function Asin((n pi x)/a)sin((n pi y)/b). sin((n pi z)/c). But if i just sub in my infinity then that doesn't really make sense, it just goes to sin(0).
     
    eit32, May 8, 2008
  5. May 8, 2008 #4

    lzkelley

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    the z portion is no longer a sin; its going to be e^ -kz for some constant k that you have to find from solving the wave equation with separation of variables.
     
    lzkelley, May 8, 2008
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