Built on Facts

Archives for November, 2010

Sunday Function

In pure mathematics there’s not too many function studied more than the Riemann zeta function. For reasons of historical tradition, the generic variable name that’s usually used is s instead of z. (The function is mostly interesting in terms of complex analysis, so x would be a bit unorthodox too.) It’s defined in the following…

Data or Dust Speck?

Shortly after the invention of the laser, a torrent of discoveries began pouring in thanks to the previously unreachable intensities that became available. Many of these discoveries fall under the general category of “nonlinear optics”, which you could more or less say is the study of the behavior of light in a medium whose optical…

Clearing the air on the Airy fuction

There was some dissension in the comments of my post on solving the Schrodinger equation with a linear potential. What the post boiled down to was that the solution was Ai(u), where we found that u was: The point of the post was to work through and get that coefficient that’s in front of the…

Sunday Function

Most textbooks, especially ones not aimed at college math majors, give a definition of “function” that seems quite intuitive. They’ll say something along the lines of: a function is a rule that takes an input x and turns it into an output f(x). Formally this isn’t quite right – the essence of a function is…

So consider the one-dimensional time-independent Schrodinger equation: In some ways it’s not really an equation as such, because you have to plug in some function V(x) that describes the potential in the problem you’re solving. When you first learn quantum mechanics you’ll learn the big ones: V(x) = 0, V(x) = V > E, V(x)…