The simplest quantum system
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...