Convergence to Planewaves for Solutions to Schrödinger's equation III
In this installment, we look at Schrödinger's equation with barriers, and study the decay of the solutions.
Convergence to Planewaves for Solutions to Schrödinger's equation II
We use Laplace transform arguments to look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation …
Convergence to Planewaves for Solutions to Schrödinger's equation
We look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation to plane waves.
Poohsticks and differential geometry
Random thought: Poohsticks illustrates well Lie differentiation
Joris' Theorem
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 …
When are curves tangent to hypersurfaces?
Given a curve and a hypersurface, both in Euclidean space, how can we tell if the curve is tangent to the hypersurface?
Torsion, curvature, and parallel transport
An expository note on the notions of curvature and torsion of a general linear connection on the tangent bundle.
A Characterization of Geodesics
About the Einstein-Infeld-Hoffmann theorem characterizing geodesics.
A Better Estimate of Kempner's Series
The Kempner series recently regained some notoriety due to a Saturday Morning Breakfast Cereal comic (the last panel). The observation …
Simulating Closed Cosmic Strings
One of my current research interests is in the geometry of constant-mean-curvature time-like submanifolds of Minkowski space. A special …