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What does infinity potential mean?

  1. Jul 16, 2010 #1
    In both http://en.wikipedia.org/wiki/Dynamical_billiards" [Broken] we have a potential who's value is infinity.

    5260159c0620fe316ca2a15b6504616b.png

    5971cea8577664b995664a37bb7721b6.png

    Now if it were just a finite number (rather than infinity), I would be getting a dirac delta function in the equations of motion (I think..) but when it's infinity I can't really do anything with it.

    So my questions are,
    • How do you derive the equations of motion using this potential?
    • What is the meaning of this infinity written here? Is it just a 'metaphor' or is there some formalism which gives it meaning?

    Thank you!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 17, 2010 #2
    It just means, that the wave function should be equal to 0 in the region where the potential is infinite. i.e. the probability to find the particle in this region is 0.

    (so you can assume a free particle where V=0 that has a 0-wave-function where V=infinity)
     
  4. Jul 17, 2010 #3
    The "infinite potential" is just a way to idealize constraints. Suppose that, for example, you constrain a particle to lie on a surface. In order to do this, we introduce a potential energy function V so high in the space that is not on the surface that the particle is constrained on the surface.

    Of course, true potential energy functions are more analytic than this. Dynamics are no longer entirely run by a simple equation of motion since collisions would have to be taken into account.

    In Classical Mechanics, this is known as "scattering theory."
     
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