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Eigensolver Project

This project provides an implementation of an automatized eigensolver to compute eigenvalues and eigenfunctions for general one-body potentials. The solver can process various potential types and plot results using included Python scripts.

Table of Contents

Features

  • Solves the eigenvalue problem for one-body Schrödinger equations.
  • Supports multiple potential types (e.g. harmonic oscillator, Gaussian, Exponential, Double-well, Modified Morse)
  • Visualizes results using Python plotting scripts.
  • Modular structure for easy extension and maintenance.

Requirements

  • Libraries:

    • MADNESS: A prerequisite library for numerical computations.

    • (As of November 22, 2024) The option DENABLE_MPI=Off does not work with the current version of the MADNESS library.

    • To ensure the project works correctly, install the MADNESS library with MPI enabled. If MPI is not installed on your system, you can install it as follows:

      • Ubuntu:
      sudo apt install openmpi-bin libopenmpi-dev
      • MacOS:
      brew install open-mpi
  • Python Packages:
    • The following Python packages are required to run the plotting scripts:
      • Numpy
      • Matplotlib (version 3.7.1)
      • Tikzplotlib
      • natsort
      • webcolors (version 1.12)

Installation

Before building the project, change the MADNESS library path in the CMakeLists.txt file to the correct path on your system. The MADNESS library path is defined in the MADNESS_DIR variable.

  1. Clone the repository:

    git clone https://git.rz.uni-augsburg.de/qalg-a/automatized_eigensolver.git

  2. Build the project:

    mkdir build_eigensolver
cd build_eigensolver
cmake ../automatized_eigensolver
make

  3. To run the eigensolver, execute the shell script run_eigensolver.sh:

    ./run_eigensolver.sh

Usage

To create a GIF of the eigenfunctions for a specific potential type, make sure that your files are organized in the following structure:

|-- build_eigensolver/
|   |-- run_eigensolver.sh
|   |-- Images/               
|   |   |-- Gaussian/
|   |   |   |-- Potential.dat
|   |   |   |-- Gaussian_Phi/
|   |   |   |   |-- Phi_0/
|   |   |   |   |   |-- phi-0-0.dat
|   |   |   |   |   |-- phi-0-1.dat
|   |   |   |   |   |-- ...
|   |   |   |   |-- Phi_1/
|   |   |   |   |   |-- phi-1-0.dat
|   |   |   |   |   |-- phi-1-1.dat
|   |   |   |   |   |-- ...
|   |   |-- Gaussian_Psi/
|   |   |   |-- Psi_0.dat
|   |   |   |-- Psi_1.dat
|   |   |   |-- ...

File Organization

  • Put the phi-*.dat files in the corresponding Phi_* folders (located inside the folder for each potential type, e.g., Gaussian_Phi).
  • Put the Psi_*.dat files in the NAME_Psi folder (e.g., Gaussian_Psi).

Plotting the Results

  1. To create the .png files for the eigenfunctions, run the run_plot_phi.sh script with the path to the Phi folder as an argument. For example:

    ./run_plot_phi.sh Images/Gaussian/Gaussian_Phi/

    This command will generate a .png file for each .dat file.

  2. After the .png files are created, you can generate a GIF by running the Python script togif.py:

    ./togif.py Images/Gaussian/Gaussian_Phi/

Project Structure

The project is organized as follows:

|-- automatized_eigensolver/
|   |-- Eigensolver/
|   |   |-- include/                <-- Header files for the eigensolver module
|   |   |   |-- ...
|   |   |-- src/                    <-- Source files for the eigensolver module
|   |   |   |-- eigensolver.cc      <-- Main implementation of the eigensolver
|   |   |-- plot/                   <-- Contains Python scripts for plotting results
|   |   |   |-- ...
|   |-- CMakeLists.txt              <-- CMake build configuration file
|-- build_eigensolver/              <-- Build directory
|   |-- run_eigensolver.sh          <-- Shell script to run the eigensolver
|   |-- Images/                     <-- Output folder for images and GIFs
|   |   |-- Gaussian/               <-- Folder for Gaussian potential type
|   |   |   |-- Potential.dat       <-- Potential data for Gaussian potential
|   |   |   |-- Gaussian_Phi/       <-- Folder for eigenfunction files (Phi)
|   |   |   |   |-- Phi_0/          <-- Folder for Phi_0 eigenfunctions
|   |   |   |   |   |-- phi-0-0.dat 
|   |   |   |   |   |-- phi-0-1.dat 
|   |   |   |   |-- Phi_1/          <-- Folder for Phi_1 eigenfunctions
|   |   |   |   |   |-- phi-1-0.dat 
|   |   |   |   |   |-- phi-1-1.dat 
|   |   |   |-- Gaussian_Psi/       <-- Folder for wavefunction files (Psi)
|   |   |   |   |-- Psi_0.dat       
|   |   |   |   |-- Psi_1.dat       
|   |   |   |   |-- ...

Explanation of Folders and Files

  • automatized_eigensolver/: Project root directory.
    • Eigensolver/: Contains source code and header files for the eigensolver module.
      • include/: Header files used for the eigensolver.
      • src/: Source files implementing the eigensolver.
      • plot/: Python scripts for visualizing results.
    • CMakeLists.txt: Build configuration file for CMake to compile the project.
  • build_eigensolver/: The build directory where compiled files and results will be stored.
    • run_eigensolver.sh: Shell script to run the eigensolver.

Needed to be created manually in the build directory:

  • Images/: Folder where output images (e.g., .png) and GIFs will be saved.
  • Gaussian/: Example folder for the Gaussian potential type, showing the expected file structure.
  • Note: Other potential types (e.g., Exponential, Double-well) should have similar folder structures within Images/.

Additional Notes

If you have any questions or need further assistance with the project, feel free to reach out. I'm happy to help!