The Tech Stack
I outline some of the technologies that I am going to use in the development of Cupcake Physics.
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Posts in Cupcake physics news
Restructuring the Site
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.
Short Break
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!
About Section
Just a small update. The website now has an About section.
Search Bar
The blog (finally) has a search bar.
A Bit of Housekeeping
There is no new material this week. However, I do go back through my old posts to add in references and updated graphics.
Comments by Disqus
You can now comment on blog posts!
Cupcake Concept Art
I show off some new concept art for future posts.
New Icons for Difficulty and Subject Area
I am rolling out new icons to help you sort through the difficulty and content of each blog post.
New Site Layout!
The Cupcake Physics blog just got a makeover!
Why I Want to Blog
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.
Posts in Video
The Electric Field Due to a Line of Charge (Part 2)
I use the general expression for the electric field around a line of charge to analyze a few special cases.
The Electric Field Due to a Line of Charge (Part 1)
I use Coulomb's law for continuous charge distributions to derive an expression for the electric field around a line segment of charge.
Charged Pendulum in an Electric Field
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.
The Velocity Selector
I go through a derivation of the speed of a charged particle that passes through a velocity selector.
Counting Double Slit Maxima
I describe how to count the theoretical maximum number of bright spots for a double slit interference experiment.
The Equilibrium Point Around Two Point Charges
I calculate the point of no electric field and no electric force around two point charges with different signs and magnitudes.
Apparent Depth and the Cartesian Sign Convention
I go through the Cartesian sign convention that is used in the derivation of apparent depth.
Electric Flux, Symmetry, and Gauss's Law
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.
Posts in Common homework problem
Guessing the Direction of Current Flow in Kirchhoff's Loop Rule
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.
Thermodynamic Properties of the Quantum Harmonic Oscillator
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.
The Molecular Zipper
I go through the famous "zipper problem", taking some time to talk about a subtle phase transition published by Charles Kittel.
Excess Charge Density in a Conductor
We know from introductory physics that excess charge within a conductor travels to its surface. How long does this process take?
The Heisenberg Equation (Part 3)
I finish my analysis of the quantum harmonic oscillator using the Heisenberg equation. This week, I focus on the famous creation and annihilation operators.
The Heisenberg Equation (Part 2)
I use the Heisenberg equation to analyze the quantum harmonic oscillator.
The Heisenberg Equation (Part 1)
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.
Small Angle Oscillations of the Double Pendulum
I go through the derivation of the normal modes of a double pendulum, simplifying the math with the small angle approximation.
An Oscillating Electron Around a Ring of Charge (Part 1)
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.
The Low Speed Limit of the Lorentz Factor
I explain how to recover the equations for Newtonian energy and momentum from the low-speed limit of the Lorentz factor.
Zooming in on the Magnifying Glass
I go through some of the properties of the simple magnifier (i.e. a magnifying glass) and derive its angular magnification.
Counting Double Slit Maxima
I describe how to count the theoretical maximum number of bright spots for a double slit interference experiment.
Falling Rope on a Scale
I derive the force exerted by a falling rope on a scale. There are many variations of this problem involving chains, sand, string, etc.
Optical Levitation of a Cylinder
I derive the maximum mass of a cylinder that can be levitated by a laser beam of a certain power.
The Equilibrium Point Around Two Point Charges
I calculate the point of no electric field and no electric force around two point charges with different signs and magnitudes.
The Electric Field Around a Charged Spherical Shell
I derive the electric field around a thin, charged spherical shell using Coulomb's law.
Apparent Depth and the Cartesian Sign Convention
I go through the Cartesian sign convention that is used in the derivation of apparent depth.
The Electromagnetic Hamiltonian
I set up the classical electromagnetic Hamiltonian and use it to derive the Lorentz force.
Breaking Degeneracy with the Spin-Orbit Interaction
I analyze some of the commutation relations in the presence of spin-orbit interaction and explain some of their consequences.
The Pauli Vector and Lie Groups - Part 2
I continue my discussion of the Pauli matrices and their relation to Lie Groups, focusing on the SU(2) group.
The Pauli Vector and Lie Groups - Part 1
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.
The Fourier Transform of the Coulomb Potential
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 Gradient of a Complex Exponential Function
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.
Posts in Applied physics
Hitting Baseballs and Blocking Swords
I spend some time analyzing a piece of advice that I received when I was learning to swordfight in the SCA.
Posts in Downloadable content
The Diffusion Equation (Part 2)
I visualize the heat kernel and explain how it is used in the diffusion equation.
Maximum Range of a Projectile
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.
The Finite Difference Method and Schrodinger's Equation
I derive the methodology behind the finite difference method and then use it to solve the one-dimensional, time-independent Schrodinger equation.
Refactoring One Year Later
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.
Posts in Derivation
Green's Function for the Two-Dimensional, Radial Laplacian
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.
Green's Function for the Three-Dimensional, Radial Laplacian
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.
Plasma Oscillations
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?
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
The Electric Field Due to a Line of Charge (Part 2)
I use the general expression for the electric field around a line of charge to analyze a few special cases.
The Electric Field Due to a Line of Charge (Part 1)
I use Coulomb's law for continuous charge distributions to derive an expression for the electric field around a line segment of charge.
Terminal Velocity
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.
Relativistic Kinetic Energy
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.
Excess Charge Density in a Conductor
We know from introductory physics that excess charge within a conductor travels to its surface. How long does this process take?
The Heisenberg Equation (Part 3)
I finish my analysis of the quantum harmonic oscillator using the Heisenberg equation. This week, I focus on the famous creation and annihilation operators.
The Heisenberg Equation (Part 2)
I use the Heisenberg equation to analyze the quantum harmonic oscillator.
The Heisenberg Equation (Part 1)
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.
Small Angle Oscillations of the Double Pendulum
I go through the derivation of the normal modes of a double pendulum, simplifying the math with the small angle approximation.
An Oscillating Electron Around a Ring of Charge (Part 3)
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.
An Oscillating Electron Around a Ring of Charge (Part 2)
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.
An Oscillating Electron Around a Ring of Charge (Part 1)
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.
The Relativistic Doppler Shift
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.
Zooming in on the Magnifying Glass
I go through some of the properties of the simple magnifier (i.e. a magnifying glass) and derive its angular magnification.
The Diffusion Equation (Part 1)
I derive and solve the diffusion equation.
The Box-Muller Algorithm
I derive the Box-Muller algorithm and visualize the random samples that it produces.
The No-Go Theorems of Quantum Information Theory (Part 3)
I finish my discussion of some of the no-go theorems in quantum information theory.
The No-Go Theorems of Quantum Information Theory (Part 2)
I continue my overview of the no-go theorems in quantum information theory.
The No-Go Theorems of Quantum Information Theory (Part 1)
I review the no-cloning theorem as well as some of the less well-known no-go theorems in quantum information theory.
A Derivation of Centripetal Force
I derive the expression for the centripetal force on a particle moving with uniform circular motion.
The Electric Field Around a Charged Spherical Shell
I derive the electric field around a thin, charged spherical shell using Coulomb's law.
Reduced Mass and Binary Star Systems - Part 3
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.
Reduced Mass and Binary Star Systems - Part 2
I derive the equations that describe the orbit of a binary star system.
Reduced Mass and Binary Star Systems - Part 1
I explain the concept of reduced mass and then demonstrate how it is used in the context of binary star systems.
Thomson's Derivation of the Larmor Formula
I review J.J. Thomson's derivation of the Larmor formula.
The Electromagnetic Hamiltonian
I set up the classical electromagnetic Hamiltonian and use it to derive the Lorentz force.
The Finite Difference Method and Schrodinger's Equation
I derive the methodology behind the finite difference method and then use it to solve the one-dimensional, time-independent Schrodinger equation.
The Pauli Vector and Lie Groups - Part 2
I continue my discussion of the Pauli matrices and their relation to Lie Groups, focusing on the SU(2) group.
Posts in Current research
The No-Go Theorems of Quantum Information Theory (Part 3)
I finish my discussion of some of the no-go theorems in quantum information theory.
The No-Go Theorems of Quantum Information Theory (Part 2)
I continue my overview of the no-go theorems in quantum information theory.
The No-Go Theorems of Quantum Information Theory (Part 1)
I review the no-cloning theorem as well as some of the less well-known no-go theorems in quantum information theory.
Posts in Interactive visual
Linear Interpolation
I visualize the method of linear interpolation on a curvy polynomial.
Newton's Cupcake
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.
The Box-Muller Algorithm
I derive the Box-Muller algorithm and visualize the random samples that it produces.
Posts in Plasma
Plasma Oscillations
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?
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
Posts in Oscillations
Plasma Oscillations
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?
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
Posts in Electromagnetic
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
Posts in Wave
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
Posts in Conductor
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
Posts in Propagation
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
Posts in Complex permittivity
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
Posts in Skin depth
An Electromagnetic Wave in a Conductor (Part 2)
What exactly does it mean to have a complex refractive index?
An Electromagnetic Wave in a Conductor (Part 1)
How does an electromagnetic wave propagate within a conductor?
Posts in Langmuir
Plasma Oscillations
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?
Posts in Waves
Plasma Oscillations
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?
Posts in Ansible
The Tech Stack
I outline some of the technologies that I am going to use in the development of Cupcake Physics.
Posts in Elixir
The Tech Stack
I outline some of the technologies that I am going to use in the development of Cupcake Physics.
Posts in Elm
The Tech Stack
I outline some of the technologies that I am going to use in the development of Cupcake Physics.
Posts in Phoenix
The Tech Stack
I outline some of the technologies that I am going to use in the development of Cupcake Physics.
