We derive the time-independent Schrödinger equation ψ(x) by applying the separation of variables method to the original form of the Schrödinger equation (time-dependent Schrödinger equation) Ψ(x,t). We explore the mathematical and physical significance and importance of the separated solution obtained this way. We also examine the method of obtaining the general solution of the Schrödinger equation as a linear combination of separated solutions.

Learn how to calculate the expectation values of position and momentum from the wave function in quantum mechanics, and extend this to the calculation formula for the expectation value of any mechanical variable Q(x,p). Then, derive the Ehrenfest theorem from this.

We examine the basic form of the Schrödinger equation, which holds a similar position in quantum mechanics as Newton's laws of motion in classical mechanics. We also explore the statistical interpretation of the physical meaning of wave functions obtained as solutions to the Schrödinger equation, perspectives on quantum indeterminacy, and the physical meaning of measurement in the Copenhagen interpretation (collapse of the wave function).

We explore the concept of reference frames and the Galilean transformation widely used in classical mechanics. We also briefly examine Maxwell's equations and the Michelson-Morley experiment, which formed the background for the emergence of the Lorentz transformation, and derive the transformation matrix of the Lorentz transformation.

Learn how to design prompts for multilingual translation of Markdown files and automate the process with Python using Anthropic/Gemini API keys. This second post in the series covers API key issuance, integration, and how to write the automation script.

This series covers setting up a container-based deep learning environment locally with NVIDIA Container Toolkit, then configuring SSH and JupyterLab so it can be used as a remote server. Part 2 walks through writing a Dockerfile and building the container image.

Learn about nuclear reaction expressions, Q-value definitions, and the concepts of mass defect and binding energy.

Briefly examine elementary particles important in nuclear engineering such as electrons, protons, neutrons, photons, and neutrinos, and explore the structure of atoms and atomic nuclei.

Part 1 of a series on building a container-based deep learning environment with NVIDIA Container Toolkit and Docker/Podman, plus SSH and JupyterLab for remote use. This post covers installing the toolkit and the container engine.

We explore the method of finding a corresponding single trigonometric function r sin(θ+α) or r cos(θ-β) for a sum of trigonometric functions in the form of f(θ) = a cos θ + b sin θ.