Quantum description of scattering

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In this video we studied about the quantum description of scattering between two spinless and non relativistic particles. In quantum mechanics the incident particle is represented by a plane wave and the target particle is represented by some potential. we assumed the scattering to be elastic.
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@ 12:08 The problem with this model is this: The moment that scattered waves are produced they will interfere with the incident waves. This means that ONLY the very first incident wave is an unaffected plane wave. Every incident wave after that is NOT FREE anymore. The next problem is that plane waves have an infinite size. So they can't represent a localized particle. A last problem is that nothing moves in this model: it is time-indepent.

jacobvandijk