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;
}