Shape changes in a wave
PROFESSOR: Next is this phenomenon that when you have a wave packet and it moves it can change shape and get distorted. And that is a very nice phenomenon that takes place in general and causes technological complications. And it's conceptually interesting. So let's discuss it. So it's still wave packets. But now we have to go back and add some time to it. So shape changes. So we had a psi of x and t is equal to 1 over square root of 2 pi phi of k e to the ikx e to the minus i omega of kt. And what did we do with this to analyze how it propagates? We expanded omega of k as omega of k0, which, again, this quantity is centered and peaks around k0, plus k minus k0 times d omega dk at k0 plus 1/2 k minus k0 squared, the second omega, dk squared at k0. And it might seem that this goes on forever. And what did we do before? We looked at this thing and we did the integral with this term and ignored the next. And with this term, we discovered that the profile moves wi...