Delta function potential I Preliminaries
PROFESSOR: Delta function potential. So it's still a one-dimensional potential-- potential is a function of x. We'll write it this way-- minus alpha delta of x, where alpha is positive. So this is a delta function in a negative direction. So if you want to draw the potential-- there's no way to draw really nicely a delta function. So you just do a thick arrow with it pointing down. It's a representation of a potential that, somehow, is rather infinite at x equals zero-- but infinite and negative. It can be thought of as the limit of a square well that is becoming deeper and deeper. And, in fact, that could be a way to analytically calculate the energy levels-- by taking carefully the limit of a potential. It is becoming thinner and thinner, but deeper and deeper, which is the way you define or regulate the delta function. You can imagine the delta function as a sequence of functions, in which it's becoming more and more narrow-- but deeper at the same ...