#### The Tech Stack

I outline some of the technologies that I am going to use in the development of Cupcake Physics.

I outline some of the technologies that I am going to use in the development of Cupcake Physics.

It's been awhile! After finishing up my thesis work and completing training at my new job, I finally have some time to devote to Cupcake Physics.

I'm in the home stretch of my Ph.D. Sadly, this means that I need to take a short break from blog posts, but I will be back in the fall!

Just a small update. The website now has an About section.

The blog (finally) has a search bar.

There is no new material this week. However, I do go back through my old posts to add in references and updated graphics.

You can now comment on blog posts!

I show off some new concept art for future posts.

I am rolling out new icons to help you sort through the difficulty and content of each blog post.

The Cupcake Physics blog just got a makeover!

This is my very first blog post. It describes what I hope to get out of this website as well as why I want to create a blog.

The electrons within a conductor are not bound to any specific atom; they are free to move around the entire crystal. What happens when you force these electrons to oscillate using an external electric field?

What exactly does it mean to have a complex refractive index?

How does an electromagnetic wave propagate within a conductor?

I use the general expression for the electric field around a line of charge to analyze a few special cases.

I use Coulomb's law for continuous charge distributions to derive an expression for the electric field around a line segment of charge.

This is a simple statics problem that combines free-body diagrams with electric force. It is often the first time that students see concepts from classical mechanics combined with concepts from electromagnetism in a non-trivial way.

I go through a derivation of the speed of a charged particle that passes through a velocity selector.

It is very easy to get your paths and currents mixed up when using Kirchhoff's loop rule. I go through a (very) simple circuit problem and demonstrate how different paths and currents will yield answers with the same magnitude, but different sign.

We know from introductory physics that excess charge within a conductor travels to its surface. How long does this process take?

I solve the differential equation that describes the motion of an oscillating electron that radiates energy. During this analysis, I describe one of the main pitfalls that people run into when using the self force.

I derive the expression for the Abraham-Lorentz force (i.e. the self-force) and set up the differential equation for the oscillatory motion of a radiating electron near a charged ring.

I calculate the electric field along the axis of a ring of charge. Then, I derive the equation of motion for an oscillating electron about the center of the ring.

I calculate the point of no electric field and no electric force around two point charges with different signs and magnitudes.

I derive the electric field around a thin, charged spherical shell using Coulomb's law.

I review J.J. Thomson's derivation of the Larmor formula.

I set up the classical electromagnetic Hamiltonian and use it to derive the Lorentz force.

I demonstrate how to take the Fourier transform of the Coulomb potential. The trick is to not use the Coulomb potential at all - instead, use the Yukawa potential.

The nuances of Gauss's law can be rather strange to students who are learning about it for the first time. I go over some of the properties of the electric flux on a Gaussian surface and why symmetry is so important.

I derive an expression for the Green's function of the two-dimensional, radial Laplacian. Anybody who read my blog post that covered the derivation of the Green's function of the three-dimensional radial Laplacian should notice a large number of similarities between the two derivations.

I derive an expression for the Green's function of the three-dimensional, radial Laplacian. I then spend some time talking about the relevant domain of the solution and how to properly verify the fundamental solution.

I visualize the method of linear interpolation on a curvy polynomial.

I continue my discussion of the Pauli matrices and their relation to Lie Groups, focusing on the SU(2) group.

I explore some of the subtle nuances of the Pauli vector that are sometimes glossed over in graduate level courses. This post will prepare us to talk about Lie groups and Lie algebras next week.

I demonstrate how to take the Fourier transform of the Coulomb potential. The trick is to not use the Coulomb potential at all - instead, use the Yukawa potential.

I spend some time commenting on one of the major difficulties that I had when I was learning undergraduate-level physics. Then, I give an example of a derivation that seems simple to upper-level students, but can be difficult for younger students to grasp if notation is not well-defined.

This is a simple statics problem that combines free-body diagrams with electric force. It is often the first time that students see concepts from classical mechanics combined with concepts from electromagnetism in a non-trivial way.

Objects don't usually fall in a vacuum! I derive an expression for the terminal velocity of a falling object for Stokes' and turbulent drag.

I go through the derivation of the normal modes of a double pendulum, simplifying the math with the small angle approximation.

Yesterday at the AAPT 2015 conference, I had a chance to attend a workshop on creating visualizations with the HTML5 canvas. I have created an interactive demonstration of Newton's cannon that launches a cupcake around the Earth.

I derive the force exerted by a falling rope on a scale. There are many variations of this problem involving chains, sand, string, etc.

I derive an expression for the horizontal distance traveled by a projectile as a function of angle. I then compare the distance traveled by a projectile launched on a flat surface versus one launched off of a cliff.

I derive the maximum mass of a cylinder that can be levitated by a laser beam of a certain power.

I derive the expression for the centripetal force on a particle moving with uniform circular motion.

I finish up the discussion of binary star systems by going over some of the properties of the equations that I derived last week. I then present the results in the context of Kepler's laws.

I derive the equations that describe the orbit of a binary star system.

I explain the concept of reduced mass and then demonstrate how it is used in the context of binary star systems.

I spend some time analyzing a piece of advice that I received when I was learning to swordfight in the SCA.

I derive the Box-Muller algorithm and visualize the random samples that it produces.

I derive the methodology behind the finite difference method and then use it to solve the one-dimensional, time-independent Schrodinger equation.

I return to a tic-tac-toe practice project that I wrote about one year ago and refactor the code. Then, I discuss three of the biggest issues that I came across while refactoring the code.

I continue my discussion of the Pauli matrices and their relation to Lie Groups, focusing on the SU(2) group.

I explore some of the subtle nuances of the Pauli vector that are sometimes glossed over in graduate level courses. This post will prepare us to talk about Lie groups and Lie algebras next week.

I finish my analysis of the quantum harmonic oscillator using the Heisenberg equation. This week, I focus on the famous creation and annihilation operators.

I use the Heisenberg equation to analyze the quantum harmonic oscillator.

First I derive the expression for the time evolution of an expectation value in quantum mechanics. Then, I derive the Heisenberg equation and compare it with the time evolution equation.

I finish my discussion of some of the no-go theorems in quantum information theory.

I continue my overview of the no-go theorems in quantum information theory.

I review the no-cloning theorem as well as some of the less well-known no-go theorems in quantum information theory.

I analyze some of the commutation relations in the presence of spin-orbit interaction and explain some of their consequences.

I go through some of the properties of the simple magnifier (i.e. a magnifying glass) and derive its angular magnification.

I describe how to count the theoretical maximum number of bright spots for a double slit interference experiment.

I derive the maximum mass of a cylinder that can be levitated by a laser beam of a certain power.

I go through the Cartesian sign convention that is used in the derivation of apparent depth.

The analysis of the quantum harmonic oscillator usually stops at finding the energy levels. In this post I take the analysis a little further, calculating some of the thermodynamic properties of a quantum harmonic oscillator.

I go through the famous "zipper problem", taking some time to talk about a subtle phase transition published by Charles Kittel.

I visualize the heat kernel and explain how it is used in the diffusion equation.

I derive and solve the diffusion equation.

The work-energy theorem is applicable outside of the domain of classical mechanics. I derive an expression for the relativistic kinetic energy gained by a particle from an incident force over some distance.

I explain how to recover the equations for Newtonian energy and momentum from the low-speed limit of the Lorentz factor.

I derive the relativistic Doppler shift equation in three different ways. The first derivation uses only the definition of time dilation. The second derivation uses a Lorentz boost along the direction of motion. The third derivation uses the general matrix formalism of special relativity.