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 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 go through the famous "zipper problem", taking some time to talk about a subtle phase transition published by Charles Kittel.
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We know from introductory physics that excess charge within a conductor travels to its surface. How long does this process take?
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 go through the derivation of the normal modes of a double pendulum, simplifying the math with the small angle approximation.
I visualize the method of linear interpolation on a curvy polynomial.
