Learn the definition and properties of second-order linear ordinary differential equations, focusing on the superposition principle for homogeneous linear ODEs and the related concept of a basis.

Calculate the energy transfer rate due to particle collisions in plasma for both elastic and inelastic collisions, and compare the magnitude of energy transfer rates for cases when the masses of the two colliding particles are similar and when they are significantly different.

We set up the Schrödinger equation for the harmonic oscillator in quantum mechanics and explore its analytical solution method. We solve the equation by introducing the dimensionless variable 𝜉, and express any normalized stationary state using Hermite polynomials.

We set up the Schrödinger equation for the harmonic oscillator in quantum mechanics and explore its algebraic solution method. We derive the wave function and energy levels of any stationary state from commutators, canonical commutation relations, and ladder operators.

Part two of our series on implementing multi-language support for a Jekyll blog with the Polyglot plugin. Learn how to add a language selector button and localize the Chirpy theme's layout for a seamless user experience.

This post introduces the process of implementing multi-language support on a Jekyll blog based on the 'jekyll-theme-chirpy' by applying the Polyglot plugin. This is the first part of the series, covering the application of the Polyglot plugin and modifications to the HTML header and sitemap.

Exploring the meaning of 'collective behavior' in the definition of plasma, examining the Saha equation, and clarifying the concept of temperature in plasma physics.

On October 31, 2024, the Claude 3.5 Sonnet model suddenly started processing given tasks with extremely low effort, causing issues with the post auto-translation system that had been working fine for the blog for the past few months. This post introduces speculations about the cause of this phenomenon and potential solutions.

For a free particle with V(x)=0, we examine the fact that the separated solution cannot be normalized and what this implies, qualitatively show the position-momentum uncertainty relation for the general solution, and derive and physically interpret the phase velocity and group velocity of Ψ(x,t).

Exploring the two generation principles of X-rays as atomic radiation, and the respective characteristics of bremsstrahlung and characteristic X-rays.