Category: C++ Computer Applications
Blog Entry © Thursday, November 13, 2025, by James Pate Williams, Jr., A* Search to Solve the 8-Tile Puzzle
Blog Entry © Monday, November 10, 2025, by James Pate Williams, Jr. More COMP 640 Advanced Computer Graphics Results
Blog Entry © Sunday, November 9, 2025, by James Pate Williams, Jr. Hydrogenic Wavefunctions, Radial Probability Functions, Distribution Functions, and First Moment Integrals
Blog Entry © Friday, October 31, 2025, by James Pate Williams, Jr. Quantum Mechanical Harmonic Oscillator Matrix Elements
// QMHOMatrixElements.cpp : Defines the entry point for the application.
//
#include "pch.h"
#include "framework.h"
#include "QMHOMatrixElements.h"
#include "Integration.h"
#define MAX_LOADSTRING 100
// Global Variables:
HINSTANCE hInst; // current instance
WCHAR szTitle[MAX_LOADSTRING]; // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING]; // the main window class name
WCHAR buffer[32768], line[128];
int n, m;
// Forward declarations of functions included in this code module:
ATOM MyRegisterClass(HINSTANCE hInstance);
BOOL InitInstance(HINSTANCE, int);
LRESULT CALLBACK WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK About(HWND, UINT, WPARAM, LPARAM);
int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
_In_opt_ HINSTANCE hPrevInstance,
_In_ LPWSTR lpCmdLine,
_In_ int nCmdShow)
{
UNREFERENCED_PARAMETER(hPrevInstance);
UNREFERENCED_PARAMETER(lpCmdLine);
// TODO: Place code here.
// Initialize global strings
LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
LoadStringW(hInstance, IDC_QMHOMATRIXELEMENTS, szWindowClass, MAX_LOADSTRING);
MyRegisterClass(hInstance);
// Perform application initialization:
if (!InitInstance (hInstance, nCmdShow))
{
return FALSE;
}
HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_QMHOMATRIXELEMENTS));
MSG msg;
// Main message loop:
while (GetMessage(&msg, nullptr, 0, 0))
{
if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
{
TranslateMessage(&msg);
DispatchMessage(&msg);
}
}
return (int) msg.wParam;
}
//
// FUNCTION: MyRegisterClass()
//
// PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
WNDCLASSEXW wcex = { };
wcex.cbSize = sizeof(WNDCLASSEX);
wcex.style = CS_HREDRAW | CS_VREDRAW;
wcex.lpfnWndProc = WndProc;
wcex.cbClsExtra = 0;
wcex.cbWndExtra = 0;
wcex.hInstance = hInstance;
wcex.hIcon = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_QMHOMATRIXELEMENTS));
wcex.hCursor = LoadCursor(nullptr, IDC_ARROW);
wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);
wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_QMHOMATRIXELEMENTS);
wcex.lpszClassName = szWindowClass;
wcex.hIconSm = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));
return RegisterClassExW(&wcex);
}
//
// FUNCTION: InitInstance(HINSTANCE, int)
//
// PURPOSE: Saves instance handle and creates main window
//
// COMMENTS:
//
// In this function, we save the instance handle in a global variable and
// create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
hInst = hInstance; // Store instance handle in our global variable
HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);
if (!hWnd)
{
return FALSE;
}
ShowWindow(hWnd, nCmdShow);
UpdateWindow(hWnd);
return TRUE;
}
static double Factorial(int n)
{
// n! = n ... 2 1
double factorial = 1.0;
for (int i = 2; i <= n; i++)
{
factorial *= i;
}
return factorial;
}
static double N(int n)
{
// normilization factor
double pi = 4.0 * atan(1.0);
double factor1 = sqrt(1.0 / pi);
double factor2 = 1.0 / (pow(2.0, n) * Factorial(n));
return sqrt(factor1 * factor2);
}
static double H(double xi, int n)
{
// Hermite polynomial
if (n == 1)
{
return 2.0 * xi;
}
else if (n == 2)
{
return 4.0 * xi * xi - 2.0;
}
else if (n == 3)
{
return xi * (8.0 * xi * xi - 12.0);
}
else if (n == 4)
{
return 16.0 * pow(xi, 4.0) - 48.0 * pow(xi, 2.0) + 12.0;
}
else if (n == 5)
{
return 32.0 * pow(xi, 5.0) - 160.0 * pow(xi, 3.0) +
120.0 * xi;
}
else if (n == 6)
{
return 64.0 * pow(xi, 6.0) - 480.0 * pow(xi, 4.0) +
720.0 * xi * xi - 120.0;
}
else if (n == 7)
{
return 128.0 * pow(xi, 7.0) - 1344.0 * pow(xi, 5.0) +
3360.0 * xi * xi * xi - 1680.0 * xi;
}
else if (n == 8)
{
return 256.0 * pow(xi, 8.0) - 3584.0 * pow(xi, 6.0) +
13440.0 * pow(xi, 4.0) - 13440.0 * xi * xi + 1680.0;
}
else if (n == 9)
{
return 512.0 * pow(xi, 9.0) - 9216.0 * pow(xi, 7.0) +
48384.0 * pow(xi, 5.0) - 80640.0 * xi * xi * xi + 30240.0 * xi;
}
else if (n == 10)
{
return 1024.0 * pow(xi, 10.0) - 23040.0 * pow(xi, 8.0) +
161280.0 * pow(xi, 6.0) - 403200.0 * pow(xi, 4.0) +
302400.0 * xi * xi - 30240.0;
}
else
{
return 0.0;
}
}
static double Psi(double xi, int n)
{
return N(n) * exp(-xi * xi / 2.0) * H(xi, n);
}
static double Dx(double xi)
{
return xi * Psi(xi, n) * Psi(xi, m);
}
static double Ex(double xi)
{
return xi * xi * Psi(xi, n) * Psi(xi, m);
}
static double Fx(double xi)
{
return pow(xi, 3.0) * Psi(xi, n) * Psi(xi, m);
}
static double Gx(double xi)
{
return pow(xi, 4.0) * Psi(xi, n) * Psi(xi, m);
}
#define IDC_COMPUTE_BUTTON 1010
#define IDC_CANCEL_BUTTON 1020
#define IDC_CLEAR_BUTTON 1030
#define IDC_EDIT_MULTILINE 1040
//
// FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
// PURPOSE: Processes messages for the main window.
//
// WM_COMMAND - process the application menu
// WM_PAINT - Paint the main window
// WM_DESTROY - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
static HFONT hFont = nullptr;
static HWND hCombo1 = nullptr;
static HWND hCombo2 = nullptr;
static HWND hCombo3 = nullptr;
static HWND hEditMultiline = nullptr;
switch (message)
{
case WM_CREATE:
CreateWindowEx(0, L"STATIC", L"n:", WS_CHILD | WS_VISIBLE,
10, 10, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo1 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 10, 120, 100, hWnd, nullptr, hInst, nullptr);
CreateWindowEx(0, L"STATIC", L"m:", WS_CHILD | WS_VISIBLE,
10, 40, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo2 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 40, 120, 150, hWnd, nullptr, hInst, nullptr);
hEditMultiline = CreateWindowEx(
WS_EX_CLIENTEDGE, // Extended style for sunken border
TEXT("EDIT"), // Class name
TEXT(""), // Initial text (can be blank)
WS_CHILD | WS_VISIBLE | WS_VSCROLL | ES_AUTOHSCROLL |
ES_LEFT | ES_MULTILINE | ES_AUTOVSCROLL | WS_HSCROLL | WS_VSCROLL,
250, 10, 600, 420, // Position and size
hWnd, // Parent window handle
(HMENU)IDC_EDIT_MULTILINE, // Unique control ID
hInst, // Application instance
NULL // Extra parameter
);
CreateWindowEx(0, L"BUTTON", L"Compute", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 80, 80, 30, hWnd, (HMENU)IDC_COMPUTE_BUTTON, hInst, NULL);
CreateWindowEx(0, L"BUTTON", L"Cancel", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 120, 80, 30, hWnd, (HMENU)IDC_CANCEL_BUTTON, hInst, NULL);
CreateWindowEx(0, L"BUTTON", L"Clear", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 160, 80, 30, hWnd, (HMENU)IDC_CLEAR_BUTTON, hInst, NULL);
hFont = CreateFont(16, 0, 0, 0, FW_BOLD, FALSE, FALSE, FALSE,
UNICODE, OUT_DEFAULT_PRECIS, CLIP_DEFAULT_PRECIS,
DEFAULT_QUALITY, DEFAULT_PITCH | FF_SWISS, L"Courier New");
SendMessage(hCombo1, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo2, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hEditMultiline, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"0");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"1");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"2");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"3");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"4");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"5");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"6");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"7");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"8");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"9");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"10");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"0");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"1");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"2");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"3");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"4");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"5");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"6");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"7");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"8");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"9");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"10");
SendMessage(hCombo1, CB_SETCURSEL, 0, 0);
SendMessage(hCombo2, CB_SETCURSEL, 0, 0);
//ShowWindow(hWnd, SW_SHOWMAXIMIZED);
buffer[0] = L'\0';
break;
case WM_COMMAND:
{
int wmId = LOWORD(wParam);
// Parse the menu selections:
switch (wmId)
{
case IDM_ABOUT:
DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
break;
case IDC_COMPUTE_BUTTON:
{
GetWindowText(hCombo1, line, 128);
std::wstring nStr(line);
n = stoi(nStr);
GetWindowText(hCombo2, line, 128);
std::wstring mStr(line);
m = stoi(mStr);
double x0 = -10.0, x1 = 10.0;
double integ1 = Integration::SimpsonsRule(1024, x0, x1, Dx);
double integ2 = Integration::SimpsonsRule(1024, x0, x1, Ex);
double integ3 = Integration::SimpsonsRule(1024, x0, x1, Fx);
double integ4 = Integration::SimpsonsRule(1024, x0, x1, Gx);
swprintf_s(line, L"n = %d\tm = %d\t(x^1) = %+lf\r\n", n, m, integ1);
wcscat_s(buffer, line);
swprintf_s(line, L"n = %d\tm = %d\t(x^2) = %+lf\r\n", n, m, integ2);
wcscat_s(buffer, line);
swprintf_s(line, L"n = %d\tm = %d\t(x^3) = %+lf\r\n", n, m, integ3);
wcscat_s(buffer, line);
swprintf_s(line, L"n = %d\tm = %d\t(x^4) = %+lf\r\n", n, m, integ4);
wcscat_s(buffer, line);
SetWindowText(hEditMultiline, buffer);
break;
}
case IDC_CLEAR_BUTTON:
buffer[0] = '\0';
SetWindowText(hEditMultiline, buffer);
break;
case IDC_CANCEL_BUTTON:
case IDM_EXIT:
DestroyWindow(hWnd);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
}
break;
case WM_PAINT:
{
PAINTSTRUCT ps;
HDC hdc = BeginPaint(hWnd, &ps);
// TODO: Add any drawing code that uses hdc here...
EndPaint(hWnd, &ps);
}
break;
case WM_DESTROY:
PostQuitMessage(0);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
return 0;
}
// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
switch (message)
{
case WM_INITDIALOG:
return (INT_PTR)TRUE;
case WM_COMMAND:
if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
{
EndDialog(hDlg, LOWORD(wParam));
return (INT_PTR)TRUE;
}
break;
}
return (INT_PTR)FALSE;
}
Blog Entry © Thursday, October 30, 2025, by James Pate Williams, Jr. Quantum Mechanical Harmonic Oscillator See Introduction to Quantum Mechanics with Applications to Chemistry by Linus Pauling and E. Bright Wilson, Jr. Chapter III
// QMHarmonicOscillator.cpp : Defines the entry point for the application.
//
#include "pch.h"
#include "framework.h"
#include "QMHarmonicOscillator.h"
#include "Integration.h"
#define MAX_LOADSTRING 100
// Global Variables:
HINSTANCE hInst; // current instance
WCHAR szTitle[MAX_LOADSTRING]; // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING]; // the main window class name
WCHAR buffer[128];
RECT rect;
bool draw = false;
int n;
std::wstring fTitle, yTitle;
std::vector<double> xi, fx;
// Forward declarations of functions included in this code module:
ATOM MyRegisterClass(HINSTANCE hInstance);
BOOL InitInstance(HINSTANCE, int);
LRESULT CALLBACK WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK About(HWND, UINT, WPARAM, LPARAM);
int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
_In_opt_ HINSTANCE hPrevInstance,
_In_ LPWSTR lpCmdLine,
_In_ int nCmdShow)
{
UNREFERENCED_PARAMETER(hPrevInstance);
UNREFERENCED_PARAMETER(lpCmdLine);
// TODO: Place code here.
// Initialize global strings
LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
LoadStringW(hInstance, IDC_QMHARMONICOSCILLATOR, szWindowClass, MAX_LOADSTRING);
MyRegisterClass(hInstance);
// Perform application initialization:
if (!InitInstance (hInstance, nCmdShow))
{
return FALSE;
}
HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_QMHARMONICOSCILLATOR));
MSG msg;
// Main message loop:
while (GetMessage(&msg, nullptr, 0, 0))
{
if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
{
TranslateMessage(&msg);
DispatchMessage(&msg);
}
}
return (int) msg.wParam;
}
//
// FUNCTION: MyRegisterClass()
//
// PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
WNDCLASSEXW wcex = { };
wcex.cbSize = sizeof(WNDCLASSEX);
wcex.style = CS_HREDRAW | CS_VREDRAW;
wcex.lpfnWndProc = WndProc;
wcex.cbClsExtra = 0;
wcex.cbWndExtra = 0;
wcex.hInstance = hInstance;
wcex.hIcon = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_QMHARMONICOSCILLATOR));
wcex.hCursor = LoadCursor(nullptr, IDC_ARROW);
wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);
wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_QMHARMONICOSCILLATOR);
wcex.lpszClassName = szWindowClass;
wcex.hIconSm = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));
return RegisterClassExW(&wcex);
}
//
// FUNCTION: InitInstance(HINSTANCE, int)
//
// PURPOSE: Saves instance handle and creates main window
//
// COMMENTS:
//
// In this function, we save the instance handle in a global variable and
// create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
hInst = hInstance; // Store instance handle in our global variable
HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);
if (!hWnd)
{
return FALSE;
}
ShowWindow(hWnd, nCmdShow);
UpdateWindow(hWnd);
return TRUE;
}
#define IDC_COMPUTE_BUTTON 1010
#define IDC_CANCEL_BUTTON 1020
#define IDC_CLEAR_BUTTON 1030
static double Factorial(int n)
{
// n! = n ... 2 1
double factorial = 1.0;
for (int i = 2; i <= n; i++)
{
factorial *= i;
}
return factorial;
}
static double N(int n)
{
// normilization factor
double pi = 4.0 * atan(1.0);
double factor1 = sqrt(1.0 / pi);
double factor2 = 1.0 / (pow(2.0, n) * Factorial(n));
return sqrt(factor1 * factor2);
}
static double H(double xi, int n)
{
// Hermite polynomial
if (n == 1)
{
return 2.0 * xi;
}
else if (n == 2)
{
return 4.0 * xi * xi - 2.0;
}
else if (n == 3)
{
return xi * (8.0 * xi * xi - 12.0);
}
else if (n == 4)
{
return 16.0 * pow(xi, 4.0) - 48.0 * pow(xi, 2.0) + 12.0;
}
else if (n == 5)
{
return 32.0 * pow(xi, 5.0) - 160.0 * pow(xi, 3.0) +
120.0 * xi;
}
else if (n == 6)
{
return 64.0 * pow(xi, 6.0) - 480.0 * pow(xi, 4.0) +
720.0 * xi * xi - 120.0;
}
else if (n == 7)
{
return 128.0 * pow(xi, 7.0) - 1344.0 * pow(xi, 5.0) +
3360.0 * xi * xi * xi - 1680.0 * xi;
}
else if (n == 8)
{
return 256.0 * pow(xi, 8.0) - 3584.0 * pow(xi, 6.0) +
13440.0 * pow(xi, 4.0) - 13440.0 * xi * xi + 1680.0;
}
else if (n == 9)
{
return 512.0 * pow(xi, 9.0) - 9216.0 * pow(xi, 7.0) +
48384.0 * pow(xi, 5.0) - 80640.0 * xi * xi * xi + 30240.0 * xi;
}
else if (n == 10)
{
return 1024.0 * pow(xi, 10.0) - 23040.0 * pow(xi, 8.0) +
161280.0 * pow(xi, 6.0) - 403200.0 * pow(xi, 4.0) +
302400.0 * xi * xi - 30240.0;
}
else
{
return 0.0;
}
}
static double I(double xi, int n)
{
// first derivative of H(x) is H'(x)
if (n == 1)
{
return 2.0;
}
else if (n == 2)
{
return 8.0 * xi;
}
else if (n == 3)
{
return 24.0 * xi * xi - 12.0;
}
else if (n == 4)
{
return 64.0 * pow(xi, 3.0) - 96.0 * xi;
}
else if (n == 5)
{
return 32.0 * 5.0 * pow(xi, 4.0) - 3.0 * 160.0 * pow(xi, 2.0) +
120.0;
}
else if (n == 6)
{
return 6.0 * 64.0 * pow(xi, 5.0) - 4.0 * 480.0 * pow(xi, 3.0) +
2.0 * 720.0 * xi;
}
else if (n == 7)
{
return 7.0 * 128.0 * pow(xi, 6.0) - 5.0 * 1344.0 * pow(xi, 4.0) +
3.0 * 3360.0 * xi * xi - 1680.0;
}
else if (n == 8)
{
return 8.0 * 256.0 * pow(xi, 7.0) - 6.0 * 13584.0 * pow(xi, 5.0) +
4.0 * 13440.0 * pow(xi, 3.0) - 2.0 * 13440.0 * xi;
}
else if (n == 9)
{
return 9.0 * 512.0 * pow(xi, 8.0) - 7.0 * 9216.0 * pow(xi, 6.0) +
5.0 * 48384.0 * pow(xi, 4.0) - 3.0 * 80640.0 * xi * xi + 30240.0;
}
else if (n == 10)
{
return 10.0 * 1024.0 * pow(xi, 9.0) - 8.0 * 23040.0 * pow(xi, 7.0) +
6.0 * 161280.0 * pow(xi, 5.0) - 4.0 * 403200.0 * pow(xi, 3.0) +
2.0 * 302400.0 * xi;
}
else
{
return 0;
}
}
static double J(double xi, int n)
{
// second derivative of H(x) is H''(x)
if (n == 2)
{
return 8.0;
}
else if (n == 3)
{
return 48.0 * xi * xi;
}
else if (n == 4)
{
return 3.0 * 64.0 * pow(xi, 2.0) - 96.0;
}
else if (n == 5)
{
return 4.0 * 32.0 * 5.0 * pow(xi, 3.0) - 2.0 * 3.0 * 160.0 * xi;
}
else if (n == 6)
{
return 5.0 * 6.0 * 64.0 * pow(xi, 4.0) - 3.0 * 4.0 * 480.0 * pow(xi, 2.0) +
2.0 * 720.0;
}
else if (n == 7)
{
return 6.0 * 7.0 * 128.0 * pow(xi, 5.0) - 4.0 * 5.0 * 1344.0 * pow(xi, 3.0) +
2.0 * 3.0 * 3360.0 * xi;
}
else if (n == 8)
{
return 7.0 * 8.0 * 256.0 * pow(xi, 6.0) - 5.0 * 6.0 * 13584.0 * pow(xi, 4.0) +
3.0 * 4.0 * 13440.0 * pow(xi, 2.0) - 2.0 * 13440.0;
}
else if (n == 9)
{
return 8.0 * 9.0 * 512.0 * pow(xi, 7.0) - 6.0 * 7.0 * 9216.0 * pow(xi, 5.0) +
4.0 * 5.0 * 48384.0 * pow(xi, 3.0) - 2.0 * 3.0 * 80640.0 * xi;
}
else if (n == 10)
{
return 9.0 * 10.0 * 1024.0 * pow(xi, 8.0) - 7.0 * 8.0 * 23040.0 * pow(xi, 6.0) +
5.0 * 6.0 * 161280.0 * pow(xi, 4.0) - 3.0 * 4.0 * 403200.0 * pow(xi, 2.0) +
2.0 * 302400.0;
}
else
{
return 0;
}
}
static double Psi(double xi, int n)
{
return N(n) * exp(-xi * xi / 2.0) * H(xi, n);
}
static void FindMinMax(
std::vector<double> x,
double& min,
double& max)
{
min = x[0];
max = x[0];
for (int i = 1; i < x.size(); i++)
{
if (x[i] < min)
min = x[i];
if (x[i] > max)
max = x[i];
}
}
static void DrawTitles(
HDC hdc, RECT clientRect, const std::wstring& fTitle,
std::wstring& yTitle, int sx0, int sx1, int sy0, int sy1)
{
HFONT hCustomFont = CreateFont(
-MulDiv(10, GetDeviceCaps(hdc, LOGPIXELSY), 72), // Height in logical units
0, // Width (0 = default)
0, // Escapement
0, // Orientation
FW_BOLD, // Weight (700 = bold)
FALSE, // Italic
FALSE, // Underline
FALSE, // StrikeOut
DEFAULT_CHARSET, // Charset
OUT_DEFAULT_PRECIS, // Output precision
CLIP_DEFAULT_PRECIS, // Clipping precision
DEFAULT_QUALITY, // Quality
FIXED_PITCH | FF_MODERN,// Pitch and family
L"Courier New" // Typeface name
);
HFONT hOldFont = (HFONT)SelectObject(hdc, hCustomFont);
SIZE sz;
int width = clientRect.right - clientRect.left;
// Title: fTitle
GetTextExtentPoint32W(hdc, fTitle.c_str(), (int)fTitle.length(), &sz);
int w = sz.cx;
int h = sz.cy;
TextOutW(hdc, (width - w) / 2, h, fTitle.c_str(), (int)fTitle.length());
// x-axis title: "x"
std::wstring xTitle = L"xi";
GetTextExtentPoint32W(hdc, xTitle.c_str(), (int)xTitle.length(), &sz);
w = sz.cx;
TextOutW(hdc, sx0 + (sx1 - sx0 - w) / 2, sy1 + 2 * h, xTitle.c_str(), (int)xTitle.length());
// y-axis title: "?"
GetTextExtentPoint32W(hdc, yTitle.c_str(), (int)yTitle.length(), &sz);
w = sz.cx;
TextOutW(hdc, sx1 + w / 5, sy0 + (sy1 - sy0) / 2 - h / 2, yTitle.c_str(), (int)yTitle.length());
SelectObject(hdc, hOldFont); // Restore original font
}
static void DrawFormattedText(HDC hdc, char loctext[], RECT rect)
{
// Draw the text with formatting options
DrawTextA(hdc, loctext, (int)strlen(loctext), &rect, DT_SINGLELINE | DT_NOCLIP);
}
static double Fx1(double xi)
{
double psi = Psi(xi, n);
return xi * psi * psi;
}
static double Fx2(double xi)
{
double psi = Psi(xi, n);
return xi * xi * psi * psi;
}
static double Fx3(double xi)
{
double psi = Psi(xi, n);
return xi * xi * xi * psi * psi;
}
static double Fx4(double xi)
{
double psi = Psi(xi, n);
return pow(xi, 4.0) * psi * psi;
}
// FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
// PURPOSE: Processes messages for the main window.
//
// WM_COMMAND - process the application menu
// WM_PAINT - Paint the main window
// WM_DESTROY - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
static HFONT hFont = nullptr;
static HWND hCombo1 = nullptr;
static HWND hCombo2 = nullptr;
static HWND hCombo3 = nullptr;
switch (message)
{
case WM_CREATE:
CreateWindowEx(0, L"STATIC", L"draw:", WS_CHILD | WS_VISIBLE,
10, 10, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo1 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 10, 120, 100, hWnd, nullptr, hInst, nullptr);
CreateWindowEx(0, L"STATIC", L"average:", WS_CHILD | WS_VISIBLE,
10, 40, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo2 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 40, 120, 150, hWnd, nullptr, hInst, nullptr);
CreateWindowEx(0, L"STATIC", L"n:", WS_CHILD | WS_VISIBLE,
10, 70, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo3 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 70, 120, 150, hWnd, nullptr, hInst, nullptr);
CreateWindowEx(0, L"BUTTON", L"Compute", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 100, 80, 30, hWnd, (HMENU)IDC_COMPUTE_BUTTON, hInst, NULL);
CreateWindowEx(0, L"BUTTON", L"Cancel", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 140, 80, 30, hWnd, (HMENU)IDC_CANCEL_BUTTON, hInst, NULL);
CreateWindowEx(0, L"BUTTON", L"Clear", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 180, 80, 30, hWnd, (HMENU)IDC_CLEAR_BUTTON, hInst, NULL);
hFont = CreateFont(16, 0, 0, 0, FW_BOLD, FALSE, FALSE, FALSE,
UNICODE, OUT_DEFAULT_PRECIS, CLIP_DEFAULT_PRECIS,
DEFAULT_QUALITY, DEFAULT_PITCH | FF_SWISS, L"Courier New");
SendMessage(hCombo1, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo2, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo3, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Hermite");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Psi");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"|Psi^2|");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"zeros");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"x");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"x^2");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"x^3");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"x^4");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"1");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"2");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"3");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"4");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"5");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"6");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"7");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"8");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"9");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"10");
SendMessage(hCombo1, CB_SETCURSEL, 0, 0);
SendMessage(hCombo2, CB_SETCURSEL, 0, 0);
SendMessage(hCombo3, CB_SETCURSEL, 0, 0);
ShowWindow(hWnd, SW_SHOWMAXIMIZED);
buffer[0] = L'\0';
break;
case WM_COMMAND:
{
int wmId = LOWORD(wParam);
// Parse the menu selections:
switch (wmId)
{
case IDM_ABOUT:
DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
break;
case IDC_COMPUTE_BUTTON:
{
if (hCombo3)
{
LRESULT result1 = SendMessage(hCombo1, CB_GETCURSEL, 0, 0);
LRESULT result2 = SendMessage(hCombo2, CB_GETCURSEL, 0, 0);
GetWindowText(hCombo3, buffer, 128);
std::wstring nStr(buffer);
n = stoi(nStr);
double x0 = -10.0, x1 = 10.0, h = (x1 - x0) / 256;
double xValue = -10.0, yValue = 0;
xi.clear();
fx.clear();
if (result1 == 0)
{
wcscpy_s(buffer, L"xi Versus Hermite Polynomial H(xi)");
fTitle = std::wstring(buffer);
wcscpy_s(buffer, L"H(xi, n)");
yTitle = std::wstring(buffer);
while (xValue <= x1)
{
xi.push_back(xValue);
yValue = H(xValue, n);
fx.push_back(yValue);
xValue += h;
}
}
else if (result1 == 1)
{
wcscpy_s(buffer, L"xi Versus Wave Function Psi(xi, n)");
fTitle = std::wstring(buffer);
wcscpy_s(buffer, L"Psi(xi, n)");
yTitle = std::wstring(buffer);
while (xValue <= x1)
{
xi.push_back(xValue);
yValue = Psi(xValue, n);
fx.push_back(yValue);
xValue += h;
}
}
else if (result1 == 2)
{
wcscpy_s(buffer, L"xi Versus |Psi^2|");
fTitle = std::wstring(buffer);
wcscpy_s(buffer, L"|Psi(xi, n)^2|");
yTitle = std::wstring(buffer);
while (xValue <= x1)
{
double psi = Psi(xValue, n);
xi.push_back(xValue);
yValue = psi * psi;
fx.push_back(yValue);
xValue += h;
}
}
GetClientRect(hWnd, &rect);
rect.left = 300;
draw = true;
InvalidateRect(hWnd, &rect, TRUE);
double integ = 0.0;
if (result2 == 0)
{
integ = Integration::SimpsonsRule(
1024, -10.0, 10.0, Fx1);
swprintf_s(buffer, L"xi * Psi^2(xi, n) = %lf", integ);
}
if (result2 == 1)
{
integ = Integration::SimpsonsRule(
1024, -10.0, 10.0, Fx2);
swprintf_s(buffer, L"xi^2 * Psi^2(xi, n) = %lf", integ);
double integ1
}
if (result2 == 2)
{
integ = Integration::SimpsonsRule(
1024, -10.0, 10.0, Fx3);
swprintf_s(buffer, L"xi^3 * Psi^2(xi, n) = %lf", integ);
}
if (result2 == 3)
{
integ = Integration::SimpsonsRule(
1024, -10.0, 10.0, Fx4);
swprintf_s(buffer, L"xi^4 * Psi^2(xi, n) = %lf", integ);
}
MessageBox(hWnd, buffer, L"Information",
MB_OK | MB_ICONINFORMATION);
}
break;
}
case IDC_CLEAR_BUTTON:
buffer[0] = '\0';
draw = false;
break;
case IDC_CANCEL_BUTTON:
case IDM_EXIT:
DestroyWindow(hWnd);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
}
case WM_PAINT:
{
if (draw)
{
PAINTSTRUCT ps;
POINT wPt = { };
HDC hdc = BeginPaint(hWnd, &ps);
double xMin = 0, yMin = 0;
double xMax = 0, yMax = 0;
FindMinMax(xi, xMin, xMax);
FindMinMax(fx, yMin, yMax);
double h = 0, pi = 0, plm = 0, theta = 0;
float xSpan = (float)(xMax - xMin);
float ySpan = (float)(yMax - yMin);
float width = (float)(rect.right - rect.left + 1);
float height = (float)(rect.bottom - rect.top - 32 + 1);
float sx0 = 2.0f * width / 16.0f + 300;
float sx1 = 14.0f * width / 16.0f + 300;
float sy0 = 2.0f * height / 16.0f;
float sy1 = 14.0f * height / 16.0f;
float deltaX = xSpan / 8.0f;
float deltaY = ySpan / 8.0f;
float xSlope = (sx1 - sx0) / xSpan;
float xInter = (float)(sx0 - xSlope * xMin);
float ySlope = (sy0 - sy1) / ySpan;
float yInter = (float)(sy0 - ySlope * yMax);
float px = 0, py = 0, sx = 0, sy = 0;
int i = 0;
float x = (float)xMin;
float y = (float)yMax;
DrawTitles(
hdc, rect, fTitle, yTitle,
(int)sx0, (int)sx1, (int)sy0, (int)sy1);
px = (float)xi[0];
py = (float)fx[0];
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
while (i <= 8)
{
sx = xSlope * x + xInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
LineTo(hdc, (int)sx, (int)sy1);
char numberStr[128] = "";
sprintf_s(numberStr, 128, "%5.4lf", x);
SIZE size = { };
GetTextExtentPoint32A(
hdc,
numberStr,
(int)strlen(numberStr),
&size);
RECT textRect = { };
textRect.left = (long)(sx - size.cx / 2.0f);
textRect.right = (long)(sx + size.cx / 2.0f);
textRect.top = (long)sy1;
textRect.bottom = (long)(sy1 + size.cy / 2.0f);
DrawFormattedText(hdc, numberStr, textRect);
x += deltaX;
i++;
}
i = 0;
y = (float)yMin;
while (i <= 8)
{
sy = ySlope * y + yInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
LineTo(hdc, (int)sx, (int)sy);
if (i != 0)
{
char numberStr[128] = "";
sprintf_s(numberStr, 128, "%+5.3lf", y);
SIZE size = { };
GetTextExtentPoint32A(
hdc,
numberStr,
(int)strlen(numberStr),
&size);
RECT textRect = { 0 };
textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
textRect.right = (long)(sx0 - size.cx / 2.0f);
textRect.top = (long)(sy - size.cy / 2.0f);
textRect.bottom = (long)(sy + size.cy / 2.0f);
DrawFormattedText(hdc, numberStr, textRect);
}
y += deltaY;
i++;
}
HGDIOBJ bPenNew = NULL;
HGDIOBJ hPenOld = NULL;
bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
hPenOld = SelectObject(hdc, bPenNew);
HRGN clipRegion = CreateRectRgn(
(int)sx0, (int)sy0, // Left, Top
(int)(sx1), (int)(sy1) // Right, Bottom
);
// Apply clipping region
SelectClipRgn(hdc, clipRegion);
px = (float)xi[0];
py = (float)fx[0];
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
wPt.x = wPt.y = 0;
MoveToEx(hdc, (int)sx, (int)sy, &wPt);
for (size_t j = 1; j < (int)xi.size(); j++)
{
px = (float)xi[j];
py = (float)fx[j];
sx = xSlope * px + xInter;
sy = ySlope * py + yInter;
LineTo(hdc, (int)sx, (int)sy);
}
DeleteObject(bPenNew);
bPenNew = NULL;
SelectObject(hdc, hPenOld);
DeleteObject(clipRegion);
EndPaint(hWnd, &ps);
}
}
break;
case WM_DESTROY:
PostQuitMessage(0);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
return 0;
}
// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
switch (message)
{
case WM_INITDIALOG:
return (INT_PTR)TRUE;
case WM_COMMAND:
if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
{
EndDialog(hDlg, LOWORD(wParam));
return (INT_PTR)TRUE;
}
break;
}
return (INT_PTR)FALSE;
}
#pragma once
class Integration
{
public:
static double TrapezoidalRule(
int n, double a, double b, double(*fx)(double));
static double SimpsonsRule(
int n, double a, double b, double(*fx)(double));
static void GenerateGaussianLegendreAbscissasAndWeights(
int n, double x[], double w[]);
static double GLIntegrate11(
int n, double x[], double w[], double(*fx)(double));
static double GLIntegrateAB(int n, double a, double b,
double x[], double w[], double(*fx)(double));
};
#include "pch.h"
#include "Integration.h"
#include "OrthogonalPolynomials.h"
#include "Zeros.h"
double Integration::TrapezoidalRule(
int n, double a, double b, double(*fx)(double))
{
double h = (b - a) / n;
double s = 0.5 * (fx(a) + fx(b));
double x = a + h;
for (int i = 1; i < n; i++)
{
s += fx(x);
x += h;
}
return h * s;
}
double Integration::SimpsonsRule(
int n, double a, double b, double(*fx)(double))
{
double h = (b - a) / n;
double h2 = 2.0 * h;
double s = 0.0;
double t = 0.0;
double x = a + h;
for (int i = 1; i < n; i += 2)
{
s += fx(x);
x += h2;
}
x = a + h2;
for (int i = 2; i < n; i += 2)
{
t += fx(x);
x += h2;
}
return h * (fx(a) + 4 * s + 2 * t + fx(b)) / 3.0;
}
void Integration::GenerateGaussianLegendreAbscissasAndWeights(
int n, double x[], double w[])
{
char name[32] = { 0 };
OrthogonalPolynomials op;
std::vector<double> roots;
Zeros::Zero("Legendre", 0.0, 0.0, n, roots);
strcpy_s(name, sizeof(name), "Legendre");
for (int i = 0; i < n; i++)
{
double xi = roots[i];
double fd = op.g(name, xi, n);
double x2 = 1.0 - xi * xi;
x[i] = xi;
w[i] = 2.0 / (x2 * fd * fd);
}
}
double Integration::GLIntegrate11(
int n, double x[], double w[], double(*fx)(double))
{
double sum = 0.0;
for (int i = 0; i < n; i++)
sum += w[i] * fx(x[i]);
return sum;
}
double Integration::GLIntegrateAB(int n, double a, double b,
double x[], double w[], double(*fx)(double))
{
double c = (b - a) / 2.0;
double d = (b + a) / 2.0;
double sum = 0.0;
for (int i = 0; i < n; i++)
sum += w[i] * fx(c * x[i] + d);
return c * sum;
}
Blog Entry © Wednesday, October 29, 2025, by James Pate Williams, Jr. Hydrogenic Atomic Spectral Lines
// HydrogenSpectralLines.cpp : Defines the entry point for the application.
//
#include "pch.h"
#include "framework.h"
#include "HydrogenSpectralLines.h"
#define MAX_LOADSTRING 100
// Global Variables:
HINSTANCE hInst; // current instance
WCHAR szTitle[MAX_LOADSTRING]; // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING]; // the main window class name
WCHAR buffer[32768], line[128], line1[128], line2[512];
double c = 299792458;
double h = 4.135667696e-15;
// Forward declarations of functions included in this code module:
ATOM MyRegisterClass(HINSTANCE hInstance);
BOOL InitInstance(HINSTANCE, int);
LRESULT CALLBACK WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK About(HWND, UINT, WPARAM, LPARAM);
int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
_In_opt_ HINSTANCE hPrevInstance,
_In_ LPWSTR lpCmdLine,
_In_ int nCmdShow)
{
UNREFERENCED_PARAMETER(hPrevInstance);
UNREFERENCED_PARAMETER(lpCmdLine);
// TODO: Place code here.
// Initialize global strings
LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
LoadStringW(hInstance, IDC_HYDROGENSPECTRALLINES, szWindowClass, MAX_LOADSTRING);
MyRegisterClass(hInstance);
// Perform application initialization:
if (!InitInstance (hInstance, nCmdShow))
{
return FALSE;
}
HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_HYDROGENSPECTRALLINES));
MSG msg;
// Main message loop:
while (GetMessage(&msg, nullptr, 0, 0))
{
if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
{
TranslateMessage(&msg);
DispatchMessage(&msg);
}
}
return (int) msg.wParam;
}
//
// FUNCTION: MyRegisterClass()
//
// PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
WNDCLASSEXW wcex = { };
wcex.cbSize = sizeof(WNDCLASSEX);
wcex.style = CS_HREDRAW | CS_VREDRAW;
wcex.lpfnWndProc = WndProc;
wcex.cbClsExtra = 0;
wcex.cbWndExtra = 0;
wcex.hInstance = hInstance;
wcex.hIcon = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_HYDROGENSPECTRALLINES));
wcex.hCursor = LoadCursor(nullptr, IDC_ARROW);
wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);
wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_HYDROGENSPECTRALLINES);
wcex.lpszClassName = szWindowClass;
wcex.hIconSm = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));
return RegisterClassExW(&wcex);
}
//
// FUNCTION: InitInstance(HINSTANCE, int)
//
// PURPOSE: Saves instance handle and creates main window
//
// COMMENTS:
//
// In this function, we save the instance handle in a global variable and
// create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
hInst = hInstance; // Store instance handle in our global variable
HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);
if (!hWnd)
{
return FALSE;
}
ShowWindow(hWnd, nCmdShow);
UpdateWindow(hWnd);
return TRUE;
}
#define IDC_COMPUTE_BUTTON 1010
#define IDC_CANCEL_BUTTON 1020
#define IDC_CLEAR_BUTTON 1030
#define IDC_EDIT_MULTILINE 1040
//
// FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
// PURPOSE: Processes messages for the main window.
//
// WM_COMMAND - process the application menu
// WM_PAINT - Paint the main window
// WM_DESTROY - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
static HFONT hFont = nullptr;
static HWND hCombo1 = nullptr;
static HWND hCombo2 = nullptr;
static HWND hCombo3 = nullptr;
static HWND hCombo4 = nullptr;
static HWND hEditMultiline = nullptr;
switch (message)
{
case WM_CREATE:
CreateWindowEx(0, L"STATIC", L"Series:", WS_CHILD | WS_VISIBLE,
10, 10, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo1 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 10, 200, 100, hWnd, nullptr, hInst, nullptr);
CreateWindowEx(0, L"STATIC", L"n2:", WS_CHILD | WS_VISIBLE,
10, 40, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo2 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 40, 120, 150, hWnd, nullptr, hInst, nullptr);
CreateWindowEx(0, L"STATIC", L"atom:", WS_CHILD | WS_VISIBLE,
10, 70, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo3 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 70, 120, 150, hWnd, nullptr, hInst, nullptr);
CreateWindowEx(0, L"STATIC", L"formula:", WS_CHILD | WS_VISIBLE,
10, 100, 80, 20, hWnd, (HMENU)IDC_STATIC, hInst, NULL);
hCombo4 = CreateWindowEx(0, L"COMBOBOX", nullptr,
WS_CHILD | WS_VISIBLE | CBS_DROPDOWNLIST | WS_VSCROLL |
ES_AUTOVSCROLL, 120, 100, 120, 150, hWnd, nullptr, hInst, nullptr);
CreateWindowEx(0, L"BUTTON", L"Compute", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 140, 80, 30, hWnd, (HMENU)IDC_COMPUTE_BUTTON, hInst, NULL);
CreateWindowEx(0, L"BUTTON", L"Cancel", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 180, 80, 30, hWnd, (HMENU)IDC_CANCEL_BUTTON, hInst, NULL);
CreateWindowEx(0, L"BUTTON", L"Clear", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 220, 80, 30, hWnd, (HMENU)IDC_CLEAR_BUTTON, hInst, NULL);
hFont = CreateFont(16, 0, 0, 0, FW_BOLD, FALSE, FALSE, FALSE,
UNICODE, OUT_DEFAULT_PRECIS, CLIP_DEFAULT_PRECIS,
DEFAULT_QUALITY, DEFAULT_PITCH | FF_SWISS, L"Courier New");
hEditMultiline = CreateWindowEx(
WS_EX_CLIENTEDGE, // Extended style for sunken border
TEXT("EDIT"), // Class name
TEXT(""), // Initial text (can be blank)
WS_CHILD | WS_VISIBLE | WS_VSCROLL | ES_AUTOHSCROLL |
ES_LEFT | ES_MULTILINE | ES_AUTOVSCROLL | WS_HSCROLL | WS_VSCROLL,
340, 10, 640, 400, // Position and size
hWnd, // Parent window handle
(HMENU)IDC_EDIT_MULTILINE, // Unique control ID
hInst, // Application instance
NULL // Extra parameter
);
SendMessage(hCombo1, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo2, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo3, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo4, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hEditMultiline, WM_SETFONT, (WPARAM)hFont, 0);
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Lyman n1 = 1 n2 >= 2");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Balmer n1 = 2 n2 >= 3");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Paschen n1 = 3 n2 >= 4");
SendMessage(hCombo1, CB_ADDSTRING, 0, (LPARAM)L"Brackett n1 = 4 n2 >= 5");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"2");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"3");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"4");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"5");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"6");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"7");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"8");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"9");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"10");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"11");
SendMessage(hCombo2, CB_ADDSTRING, 0, (LPARAM)L"12");
SendMessage(hCombo1, CB_SETCURSEL, 0, 0);
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"hydrogen");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"helium+");
SendMessage(hCombo3, CB_ADDSTRING, 0, (LPARAM)L"lithium++");
SendMessage(hCombo4, CB_ADDSTRING, 0, (LPARAM)L"energy eV");
SendMessage(hCombo4, CB_ADDSTRING, 0, (LPARAM)L"frequency Hz");
SendMessage(hCombo4, CB_ADDSTRING, 0, (LPARAM)L"wavelength A");
SendMessage(hCombo1, CB_SETCURSEL, 0, 0);
SendMessage(hCombo2, CB_SETCURSEL, 0, 0);
SendMessage(hCombo3, CB_SETCURSEL, 0, 0);
SendMessage(hCombo4, CB_SETCURSEL, 0, 0);
buffer[0] = L'\0';
break;
case WM_COMMAND:
{
int wmId = LOWORD(wParam);
// Parse the menu selections:
switch (wmId)
{
case IDM_ABOUT:
DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
break;
case IDC_COMPUTE_BUTTON:
{
int n1 = 0, n2 = 0;
WCHAR series[16] = { 0 };
if (hCombo1)
{
GetWindowText(hCombo1, line, 128);
}
if (std::wcsstr(line, L"Lyman"))
{
wcscpy_s(series, L"Lyman");
n1 = 1;
}
else if (std::wcsstr(line, L"Balmer"))
{
wcscpy_s(series, L"Balmer");
n1 = 2;
}
else if (std::wcsstr(line, L"Paschen"))
{
wcscpy_s(series, L"Paschen");
n1 = 3;
}
else if (std::wcsstr(line, L"Brackett"))
{
wcscpy_s(series, L"Brackett");
n1 = 4;
}
if (hCombo2)
{
GetWindowText(hCombo2, line, 128);
std::wstring n2Str(line);
n2 = stoi(n2Str);
}
if (n2 < n1 + 1)
{
MessageBox(hWnd, L"n2 must be greater than equal n1 + 1",
L"Warning", MB_OK | MB_ICONWARNING);
break;
}
double Z = 1.0;
GetWindowText(hCombo3, line, 128);
if (wcscmp(line, L"hydrogen") == 0)
{
Z = 1.0;
}
else if (wcscmp(line, L"helium+") == 0)
{
Z = 2.0;
}
else if (wcscmp(line, L"lithium++") == 0)
{
Z = 3.0;
}
double deltaE = -13.6 * Z * Z * (1.0 / (n1 * n1) - 1.0 / (n2 * n2));
double nu = deltaE / h;
double lambda = c / nu / 1.0e-10;
double number = deltaE;
GetWindowText(hCombo4, line1, 128);
if (wcscmp(line1, L"energy eV") == 0)
{
number = deltaE;
}
else if (wcscmp(line1, L"frequency Hz") == 0)
{
number = nu;
}
else if (wcscmp(line1, L"wavelength A") == 0)
{
number = lambda;
}
swprintf_s(line2, L"%s\t%s\t%s\t%d\t%d\t%lf\r\n",
series, line, line1, n1, n2, number);
wcscat_s(buffer, line2);
if (hEditMultiline)
{
SetWindowText(hEditMultiline, buffer);
}
break;
}
case IDC_CLEAR_BUTTON:
buffer[0] = '\0';
SetWindowText(hEditMultiline, buffer);
break;
case IDC_CANCEL_BUTTON:
case IDM_EXIT:
DestroyWindow(hWnd);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
}
break;
case WM_PAINT:
{
PAINTSTRUCT ps;
HDC hdc = BeginPaint(hWnd, &ps);
// TODO: Add any drawing code that uses hdc here...
EndPaint(hWnd, &ps);
}
break;
case WM_DESTROY:
PostQuitMessage(0);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
return 0;
}
// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
switch (message)
{
case WM_INITDIALOG:
return (INT_PTR)TRUE;
case WM_COMMAND:
if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
{
EndDialog(hDlg, LOWORD(wParam));
return (INT_PTR)TRUE;
}
break;
}
return (INT_PTR)FALSE;
}
Blog Entry © Thursday, October 23, 2025, by James Pate Williams, Jr. A Stochastic ProblemRelated to the Subset Sum Problem
Blog Entry © Tuesday, October 21, 2025, by James Pate Williams, Jr., Solving Low Density Subset Sum Problems Using the LLL-Lattice Reduction Algorithm
// Algorithm found in the "Handbook of
// Applied Cryptography" (c) 1997 by
// Alfred J. Menezes, Paul C van Oorschot,
// and Scott Vanstone 3.105 Algorithm
// Chapter 3 pages 120 - 121
#pragma once
class LLL_Lattice
{
private:
static double Scalar(
int n,
std::vector<double> u,
std::vector<double> v);
static void RED(
int k, int l, int n,
std::vector<std::vector<double>>& b,
std::vector<std::vector<double>>& h,
std::vector<std::vector<double>>& mu);
static void SWAP(
int k, int k1, int kmax, int n,
double m, std::vector<double>& B,
std::vector<std::vector<double>>& b,
std::vector<std::vector<double>>& bs,
std::vector<std::vector<double>>& h,
std::vector<std::vector<double>>& mu);
public:
static bool LLL(
int n,
std::vector<std::vector<double>>& b,
std::vector<std::vector<double>>& h);
};
#include "pch.h"
#include "LLL_Lattice.h"
double LLL_Lattice::Scalar(
int n,
std::vector<double> u,
std::vector<double> v)
{
// Calculate the scalar product of two vectors [1..n]
double sum = 0.0;
for (int i = 1; i <= n; i++) sum += u[i] * v[i];
return sum;
}
void LLL_Lattice::RED(
int k, int l, int n,
std::vector<std::vector<double>>& b,
std::vector<std::vector<double>>& h,
std::vector<std::vector<double>>& mu)
{
int i, q = (int)(0.5 + mu[k][l]);
if (fabs(mu[k][l]) > 0.5)
{
for (i = 1; i <= n; i++)
{
b[k][i] -= q * b[l][i];
h[i][k] -= q * h[i][l];
}
mu[k][l] -= q;
for (i = 1; i <= l - 1; i++)
{
mu[k][i] -= q * mu[l][i];
}
}
}
void LLL_Lattice::SWAP(
int k, int k1, int kmax, int n,
double m, std::vector<double>& B,
std::vector<std::vector<double>>& b,
std::vector<std::vector<double>>& bs,
std::vector<std::vector<double>>& h,
std::vector<std::vector<double>>& mu)
{
double C, t;
int i, j;
std::vector<double> c(n + 1);
for (j = 1; j <= n; j++)
{
t = b[k][j];
b[k][j] = b[k1][j];
b[k1][j] = t;
t = h[j][k];
h[j][k] = h[j][k1];
h[j][k1] = t;
}
if (k > 2)
{
for (j = 1; j <= k - 2; j++)
{
t = mu[k][j];
mu[k][j] = mu[k1][j];
mu[k1][j] = t;
}
}
C = B[k] + m * m * B[k1];
mu[k][k1] = m * B[k1] / C;
for (i = 1; i <= n; i++)
{
c[i] = bs[k1][i];
}
for (i = 1; i <= n; i++)
{
bs[k1][i] = bs[k][i] + m * c[i];
}
for (i = 1; i <= n; i++)
{
bs[k][i] = -m * bs[k][i] + B[k] * c[i] / C;
}
B[k] *= B[k1] / C;
B[k1] = C;
for (i = k + 1; i <= kmax; i++)
{
t = mu[i][k];
mu[i][k] = mu[i][k1] - m * t;
mu[i][k1] = t + mu[k][k1] * mu[i][k];
}
}
bool LLL_Lattice::LLL(
int n,
std::vector<std::vector<double>>& b,
std::vector<std::vector<double>>& h)
{
// Lattice reduction algorithm
double m;
std::vector<double> B(n + 1);
std::vector<double> bv(n + 1);
std::vector<double> bw(n + 1);
std::vector<std::vector<double>> bs(n + 1,
std::vector<double>(n + 1));
std::vector<std::vector<double>> mu(n + 1,
std::vector<double>(n + 1));
int i, j, k, k1, kmax = 1, l;
for (i = 1; i <= n; i++)
bv[i] = bs[1][i] = b[1][i];
B[1] = Scalar(n, bv, bv);
for (i = 1; i <= n; i++)
{
for (j = 1; j <= n; j++)
{
h[i][j] = 0.0;
}
h[i][i] = 1.0;
}
for (k = 2; k <= n; k++)
{
if (k <= kmax)
goto Label3;
kmax = k;
for (i = 1; i <= n; i++)
{
bs[k][i] = b[k][i];
}
for (j = 1; j <= k - 1; j++)
{
for (l = 1; l <= n; l++)
{
bv[l] = b[k][l];
bw[l] = bs[j][l];
}
mu[k][j] = Scalar(n, bv, bw) / B[j];
for (i = 1; i <= n; i++)
{
bs[k][i] -= mu[k][j] * bs[j][i];
}
}
for (i = 1; i <= n; i++)
{
bv[i] = bs[k][i];
}
B[k] = Scalar(n, bv, bv);
if (B[k] == 0.0)
return false;
Label3:
k1 = k - 1;
m = mu[k][k1];
RED(k, k1, n, b, h, mu);
if (B[k] < (0.75 - m * m) * B[k1])
{
SWAP(k, k1, kmax, n, m, B, b, bs, h, mu);
k = max(2, k1);
goto Label3;
}
for (l = k - 2; l >= 1; l--)
{
RED(k, l, n, b, h, mu);
}
}
return true;
}
Numerical Explorations 