Mathematical Diversions

A collection of mathematical miscellany that diverts me from my main research interests. Some of the posts are interesting (to me) mathematical problems with their solutions. Others are mostly recreational things that distracted me at one time or another. The intended audience for posts in this category are my sole self, and so I make no great effort to polish the writing. Do send me an email with questions if you find anything here interesting or confusing.

The "Nirenberg trick" or "Nirenberg transformation" is the observation1 that the semilinear wave equation …

In this installment, we look at Schrödinger's equation with barriers, and study the decay of the solutions.

We use Laplace transform arguments to look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation …

We look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation to plane waves.

Random thought: Poohsticks illustrates well Lie differentiation

A proof is given of Joris' theorem, which states that if two coprime powers of a function are both smooth, then so is the original …

Given a curve and a hypersurface, both in Euclidean space, how can we tell if the curve is tangent to the hypersurface?

An expository note on the notions of curvature and torsion of a general linear connection on the tangent bundle.

One of my current research interests is in the geometry of constant-mean-curvature time-like submanifolds of Minkowski space. A special …

Numpy simulation of how classical and quantum particles interact with potential barriers.