Algebra Quadratic Equations of Complex Numbers
This article considers a method for solving quadratic equations over complex numbers, as I thought it might be necessary when solving the Dirac equation numerically.
kaname.hirano
Algebra 
Analysis Numerical Solution of the Schrödinger Equation
This article explains the finite difference method as a numerical solution of the Schrödinger equation. We show the results of calculations for the case of free particles and one-dimensional Coulomb potential.
Physics Schrödinger Equation for One-dimensional Coulomb Potential
This article presents an unconventional solution to the Schrödinger equation in the presence of a one-dimensional Coulomb potential.
Analysis Distance on a Sphere
This article considers distances on a sphere and compare their properties with those in Euclidean space. We present the hypothesis that distances in gravity may not be exactly distances in Euclidean space, but may be approximations of distances on a sphere.
Physics Gravity in One-dimensional Space
This article considers gravity when space is one-dimensional. I believe that by expanding this to what happens when it becomes two-dimensional, and then three-dimensional, I will be able to arrive at the true essence of gravity.
Analysis Numerical Solution of Ordinary Differential Equations
This article will provide an overview of the Euler method and the Runge-Kutta method as numerical methods for solving ordinary differential equations with initial conditions. For equations that cannot be solved analytically, we will use numerical methods to explain them.
Physics Elliptical Motion in the Theory of Relativity
This article derives an equation of motion equivalent to the Schwarzschild solution from the theory of analytical mechanics in a conical coordinate system.
Probability Probability Distribution on the Sphere
This article consider a probability distribution that is uniformly distributed on a sphere. In the case of a two-dimensional sphere, the probability distribution of each coordinate has a uniform distribution, and has some interesting properties.
Physics Two-body Problem
This article consider how the equations of motion for elliptical motion in classical mechanics, known as the two-body problem, can be formulated by rewriting the equations as if two masses were moving independently.
Probability How Machine Learning Works
Although it may seem a little late to be saying this, I feel like I've finally come to understand what makes machine learning different from other data analysis methods such as regression analysis and how it works, so I'll give a brief explanation here.