Open course ware

PROFESSOR: The simplest quantum system. In order to decide what could be the simplest quantum system you could say a particle in a box. It's very simple, but in a sense it's not all that simple. It has infinitely many states. All these functions on an interval, and then the energy is where infinitely many of them, so not that simple. OK, infinite bound says something with one bound. OK, a delta function potential just one bound state, but it has infinitely many scattering states. It's still complicated. What could be simpler? Suppose you have the Schrodinger equation. H psi. And we work in general we know that this thing has energy eigenstates, and probably we should focus on them. So Psi equal E to the minus I, Et over H bar. Little psi, and then have H Psi equal E psi. That is quantum mechanics, and you could say, well it's up to me to decide what the Hamiltonian is. If I want to invent the simplest quantum mechanical system. On the other hand, there are...

PROFESSOR: The simplest bound that a random variable differs by much from its expectation is due to a guy named Markov, a Russian probability theorist. And this is Markov's bound that we're going to talk about. Let's illustrate it with a memorable example of IQ. In the MIT context, it may be a radical idea. But IQ was this thing that was invented for intelligence quotient in the late 19th century, I believe. Might have been early 20th. It was meant as an effort to break the mold at Harvard of hiring the children of wealthy alumni. And the idea was to have merit-based admissions. And it was going to be some objective measure that did not depend on social class of the ability that people had. And Harvard was going to admit students based on merit and their intelligence quotient. So the original design of the intelligent quotient by a bunch of psychologists was that the average was supposed to be 100 over the whole population, which, of course, is-- around here, ...