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PROFESSOR: We'll begin by discussing the wave packets and uncertainty. So it's our first look into this Heisenberg uncertainty relationships. And to begin with, let's focus it as fixed time, t equals zero. So we'll work with packets at t equals zero. And I will write a particular wave function that you may have at t equals 0, and it's a superposition of plane waves. So it would be e to the ikx. You sum over many of them, so you're going to sum over k, but you're going to do it with a weight, and that's 5k. And there's a lot to learn about this, but the physics that is encoded here is that any wave at time equals 0, this psi of x at time equals 0, can be written as a superposition of states with momentum h bar k. You remember e to the ikx represents a particle or a wave that carries momentum h bar k. So this whole idea here of a general wave function being written in this way carries physical meaning for us. It's a quantum mechanical...

PROFESSOR: Let me begin by introducing the subject. The subject is resonances. And we have seen, actually, a little bit of this in the resonant transmission of the Ramsauer-Townsend effect. Because of a resonance phenomenon within the square well obstacle, somehow, for some particular frequencies, for some particular energies, the particles were able to zoom by without experiencing any reflection, whatsoever. So let's begin the subject of resonances by asking a question. If you have the usual potential, the short range potential, which means, that for some distance, R, greater than 0, the potential is 0. Here we put a barrier, and over there could be anything, some potential. We've computed some-- this concept of time delay, there's a formula for the time delay. In fact, it was given by 2 h bar d delta dE, the time delay, 2 h bar d delta dE. And we discussed that this time delay can be positive or it can be negative. If it's positive, it really means a tim...

following content is provided by MIT OpenCourseWare under a Creative Commons license additional information about our license and MIT opencourseware in general is available at ocw.mit.edu what I want to do today is to give you the maximum amount of time to indicate what you've got out of the course and how that is related to your second paper which is due today but for which I will give interview and extension that we will determine later on the maximum possible extension the reason I want you to have as much time as possible and that there is no reading for today is in order for you to make that paper something that you will be proud of in the present in you and in the future in the meantime what I want to do is to first give you a very brief idea of what I at least was hoping to do in the course then make a few remarks about filming so last week the Seventh Seal of England Bergman have some discussion with you about that but most of the time to vote to your individu...

HiJohn Guttag. By day, I'm a professor of Electrical Engineering and Computer Science at MIT and also a member of the Computer Science and Artificial Intelligence Laboratory at MIT. But you probabaly know me as the figurehead or something behind 6.00 and the whole series of 6.00 courses. It's a really good question about what keeps a learner interested in pursuing this topic. We designed this course actually to be a hard course. It's very similar to what we teach at MIT. And we really didn't want to compromise on the opportunity for students to learn alot. However, as it's been said there's no royal road to mathematics. There's no royal road to computer science. To learn a lot, you actually have to work. On campus, we are able to provide the students who are struggling a lot of interaction and counseling and dare I say it hand-holding to encourage them to keep going. It's much harder to do that when we don't physically meet with the stu...