Analysis
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.
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.
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.
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.
Analysis Kepler Equation
The orbits of planets and other objects moving around stars are elliptical, but the angular velocity is not constant. We consider a method of finding a solution to an algebraic equation called the Kepler equation by using Bessel functions.
Analysis Bessel Functions
Here is a brief summary of the properties of Bessel functions. They will be necessary when considering Kepler's equations (equations of elliptical motion) and the motion of electrons bound to atomic nuclei.
Analysis Complex Functions and Schrödinger Equation
A short story about the title of the author's book "Complex Functions and the Schrödinger Equation".