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!