Category: Computer Science
New and Corrected Ground State Energy Numerical Computation for the Helium Like Atom (Atomic Number 2) by James Pate Williams, Jr.
A New Calculus of Variations Solution of the Schrödinger Equation for the Lithium Like Atom’s Ground State Energy
This computation took a lot longer time to reach a much better solution than my previously published result.
A Calculus of Variations Solution to the Quantum Mechanical Schrödinger Wave Equation for the Lithium Like Atom (Atomic Number Z = 3) by James Pate Williams, Jr.
My New Ordnance Pamphlet 770 Calculations by James Pate Williams, Jr. © November 12, 2023
Guitar String and Piano Key Frequencies by James Pate Williams, Jr.
// FrequencyKey.cpp : Defines the entry point for the console application.
// James Pate Willims, Jr. (c) All Applicable Rights Reserved
#include "stdafx.h"
#include <math.h>
#include <iomanip>
#include <iostream>
#include <string>
#include <vector>
using namespace std;
vector<string> pnote;
double a = pow(2.0, 1.0 / 12.0);
double f0 = 440.0, gStrF[6];
double e2, a2, d3, g3, b3, e4;
double pfreq[9 * 12];
int offset = 0;
double fn(int n)
{
return f0 * pow(a, n);
}
void printFrequency(char note, int octave, double frequency)
{
cout << note << "\t" << octave << "\t";
cout << setw(6) << fixed << setprecision(2);
cout << frequency << endl;
}
int main()
{
for (int octave = 0; octave <= 8; octave++)
{
pnote.push_back("C");
pnote.push_back("C#");
pnote.push_back("D");
pnote.push_back("D#");
pnote.push_back("E");
pnote.push_back("F");
pnote.push_back("F#");
pnote.push_back("G");
pnote.push_back("G#");
pnote.push_back("A");
pnote.push_back("A#");
pnote.push_back("B");
}
pfreq[0] = 16.35;
pfreq[1] = 17.32;
pfreq[2] = 18.35;
pfreq[3] = 19.45;
pfreq[4] = 20.6;
pfreq[5] = 21.83;
pfreq[6] = 23.12;
pfreq[7] = 24.5;
pfreq[8] = 25.96;
pfreq[9] = 27.5;
pfreq[10] = 29.14;
pfreq[11] = 30.87;
for (int octave = 1; octave <= 8; octave++)
{
for (int i = 0; i < 12; i++)
{
pfreq[octave * 12 + i] = 2.0 * pfreq[(octave - 1) * 12 + i];
}
}
gStrF[0] = e2 = fn(offset - 29);
gStrF[1] = a2 = fn(offset - 24);
gStrF[2] = d3 = fn(offset - 19);
gStrF[3] = g3 = fn(offset - 14);
gStrF[4] = b3 = fn(offset - 10);
gStrF[5] = e4 = fn(offset - 5);
cout << "Guitar\tOctave\tFrequency (Hz)" << endl;
printFrequency('E', 2, e2);
printFrequency('A', 2, a2);
printFrequency('D', 3, d3);
printFrequency('G', 3, g3);
printFrequency('B', 3, b3);
printFrequency('E', 4, e4);
cout << endl;
cout << "Piano Keys" << endl << endl;
for (int octave = 0; octave <= 8; octave++)
{
for (int i = 0; i < 2; i++)
{
cout << octave << '\t';
for (int j = 0; j < 6; j++)
{
{
cout << pnote[(12 * octave + 6 * i + j) % 12] << '\t';
cout << pfreq[(12 * octave + 6 * i + j)] << '\t';
}
}
cout << endl;
}
}
return 0;
}
Pollard-Shor-Williams Factor Method by James Pate Williams, Jr.
This factoring algorithm is based on Pollard’s rho, Shor’s classical, and my modification of the two preceding methods.
Lucas-Lehmer Primality Test in C Utilizing Arjen K. Lenstra’s FreeLIP (Free Large Integer Package) by James Pate Williams, Jr.
C# Three-Dimensional Cartesian Vector Calculator (c) September 24, 2023, by James Pate Williams, Jr. All Applicable Rights Reserved
I wrote and debugged this C# code after I found out that my 1989 vector calculator in Modula-2 for the Commadore Amiga 2000 was not working correctly.
// C# Three-Dimensional Cartesian Vector Calculator
// (c) September 24, 2023 by James Pate Williams, Jr.
// All Applicable Rights Reserved
using System;
using System.Windows.Forms;
namespace CSVectorCalculator
{
public partial class MainForm : Form
{
public MainForm()
{
InitializeComponent();
}
private static double[] A = new double[3];
private static double[] B = new double[3];
private static double[] C = new double[3];
private void ValidateAB(
ref bool valid)
{
try
{
A[0] = double.Parse(textBox1.Text);
A[1] = double.Parse(textBox2.Text);
A[2] = double.Parse(textBox3.Text);
B[0] = double.Parse(textBox4.Text);
B[1] = double.Parse(textBox5.Text);
B[2] = double.Parse(textBox6.Text);
valid = true;
}
catch (Exception ex)
{
MessageBox.Show(ex.Message, "Warning",
MessageBoxButtons.OK, MessageBoxIcon.Warning);
valid = false;
}
}
private void FillC(double[] C)
{
textBox7.Text = C[0].ToString();
textBox8.Text = C[1].ToString();
textBox9.Text = C[2].ToString();
}
private void button1_Click(object sender, EventArgs e)
{
bool valid = true;
ValidateAB(ref valid);
if (valid)
{
C[0] = A[0] + B[0];
C[1] = A[1] + B[1];
C[2] = A[2] + B[2];
FillC(C);
}
}
private void button2_Click(object sender, EventArgs e)
{
bool valid = true;
ValidateAB(ref valid);
if (valid)
{
C[0] = A[0] - B[0];
C[1] = A[1] - B[1];
C[2] = A[2] - B[2];
FillC(C);
}
}
private void button3_Click(object sender, EventArgs e)
{
bool valid = true;
ValidateAB(ref valid);
if (valid)
{
C[0] = A[1] * B[2] - A[2] * B[1];
C[1] = A[0] * B[2] - A[2] * B[0];
C[2] = A[1] * B[0] - A[0] * B[1];
FillC(C);
}
}
private void button4_Click(object sender, EventArgs e)
{
bool valid = true;
ValidateAB(ref valid);
if (valid)
{
C[0] = A[0] * B[0] + A[1] * B[1] + A[2] * B[2];
C[1] = C[2] = 0.0;
FillC(C);
}
}
private void button5_Click(object sender, EventArgs e)
{
bool valid = true;
ValidateAB(ref valid);
if (valid)
{
C[0] = Math.Sqrt(A[0] * A[0] + A[1] * A[1] + A[2] * A[2]);
C[1] = C[2] = 0.0;
FillC(C);
}
}
private void button6_Click(object sender, EventArgs e)
{
bool valid = true;
ValidateAB(ref valid);
if (valid)
{
textBox1.Text = C[0].ToString();
textBox2.Text = C[1].ToString();
textBox3.Text = C[2].ToString();
C[0] = C[1] = C[2] = 0.0;
FillC(C);
}
}
}
}
Numerical Explorations 