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Gaussian packet, very large countable set, throwaway half, still good Gaussian?

  1. Nov 5, 2014 #1
    Say we do physics in a very large box of side L. Using the proper superposition of a countable number of momentum eigen states can we write down the wave function of a localized high energy particle in a box?

    If so, assume the number of superposed momentum states is N. Now randomly throw away half the N momentum states. Is the resultant superposition still nearly a localized high energy particle? How much can be thrown away, if any, and still have a pretty good Gaussian? If I have a superposition of a trillion momentum eigen states and I throw away one what harm did I do?

    Thanks for any help!
     
  2. jcsd
  3. Nov 5, 2014 #2

    bhobba

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    They are eigenstates of energy - not momentum.

    But by means of a Fourier transform you can go to the momentum representation - but you have just changed the representation - not the fact you have countable eigenstates:
    http://en.wikipedia.org/wiki/Particle_in_a_box

    If you throw away any - one - a million - it doesn't matter - its not the correct solution. Practically - well that depends on the situation.

    Thanks
    Bill
     
    Last edited: Nov 5, 2014
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