Solving the Schrödinger Equation with Numerov’s Algorithm

The Schrödinger equation describes the energy and time-evolution of a particle or system of particles, and is one of the fundamental building blocks of modern physics. In it’s general form, the (time-independent) Schrödinger equation looks like this:

\(\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial x^2}\psi(x) + V(x) \psi(x) = E\psi(x)\)

There are relatively few situations in which the Schrödinger equation can be solved analytically, and numerical methods and approximations are one way around that analytical limitation. To demonstrate how this is possible and how a numerical solution works, what better way than to solve a system which can be solved analytically and comparing the results. Continue reading

Physics Bungee-Rope Cursor Trailer

I’m getting ready for starting a course in computational physics, and so, ignoring the fact I’m meant to be revising for an exam this Monday, I thought I’d prepare for the more exciting of the two. I’ve always wanted to code this little physics model ever since I saw it on one of those JavaScript snippet websites back when dial-up was fast and people downloaded mp3s one at a time. Those were the days.

Well, I never made it mainly because I didn’t understand how. Could this be the best thing my physics degree has taught me thus far? Continue reading