# Dispersive PDE

A dispersive partial differential equation is one where solutions tend to spread out, due to waves with different frequencies traveling at different phase velocities. As a result, finite energy solutions tend to decay in amplitude, and solutions can be frequently more regular than the initial data. Examples of such equations include Schrödinger's equation, the Klein-Gordon equation, the Korteweg de-Vries equation (and many other equations governing surface waves on fluid interfaces), and the wave equation in dimensions > 1.

### 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.

### Shooting particles with Python

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