Localized High Energy Particle in a Box: Examining Superposition Limits

[Spinnor]

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!

 

[bhobba]

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?

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