ruvi.blog

Introduction # Harmonic oscillators are good model for a very wide class of systems.

Introduction # ... quaternions appear to exude an air of nineteenth century decay, as a rather unsuccessful species in the struggle-for-life of mathematical ideas.

Introduction # In this post we will find a simple expression for integer powers of any two-by-two matrix $$\mathbf{M}$$.

This is a guest post by Andrew Jamieson, based on a problem we solved together.

Introduction # This post has been expanded to a full set of tutorials on FPGA programming with the Red Pitaya!

Introduction # In this post we'll go through a very useful technique for solving linear differential equations: the differential operator method.

Introduction # Many systems are described by second-order Hamiltonians.

Introduction # In a previous post we saw how entropy quantifies the 'volume' occupied by a discrete random variable.

Introduction # This is the first in a series of posts which introduce classical information theory using the geometric framework — in contrast to the often-used viewpoint of binary bits.

Let's apply the material from the post on boundary conditions to calculate a transfer matrix.

Introduction # In a previous post we looked at the geometric meaning of Maxwell's equations: $$ \nabla\cdot \mathbf{B}=0; \;\nabla\times \mathbf{E}+\frac{\partial \mathbf{B}}{\partial t}=0, $$ $$ \nabla\cdot \mathbf{E}=\frac{\rho}{\epsilon_0}; \; \nabla\t…

Introduction # Let's take a look at Maxwell's equations (in differential form): $$ \nabla\cdot \mathbf{B}=0;\;\nabla\times \mathbf{E}+\frac{\partial \mathbf{B}}{\partial t}=0,$$ $$ \nabla\cdot \mathbf{E}=\frac{\rho}{\epsilon_0};\; \nabla\times \mathbf{B}-…

Introduction # Many people are familiar with the so-called 'Feynmann's trick' of differentiating under the integral which greatly simplifies some integration and series problems.

Introduction # In this article we will introduce superdense coding, a scheme which lets Alice send two bits of (classical) information to Bob by transmitting a single entangled qubit.