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Classically determining velocity of particle in a box

  1. Sep 22, 2011 #1
    1. The problem statement, all variables and given/known data
    I am supposed to show, using a classical argument, that the speed "v" of a particle in an infinite 1-D potential well is

    v= (nh)/(2mL)


    2. Relevant equations



    3. The attempt at a solution
    Doesn't the particle just reflect back and forth against the walls of the well with a constant speed that it was given initially? How can I classically argue that planck's constant is supposed to be in the velocity?
     
  2. jcsd
  3. Sep 22, 2011 #2

    dynamicsolo

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    OK, it's "semi-classical": you use the classical concept of linear momentum ( p = mv ) , together with deBroglie's result for "particle wavelength" [itex] \lambda = \frac{h}{p} .[/itex]

    Since the potential well is "infinitely high", it has "hard walls", which we've placed at a separation L . What sort of wave will constructive interference permit in such a "box"? What are the possible wavelengths?
     
  4. Sep 22, 2011 #3
    oh, that makes perfect sense. thanks!
     
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