🚀 Schrödinger Equation Simulator in 1D and 2D

An interactive simulator for solving the time-dependent Schrödinger equation in confined quantum systems, using advanced numerical methods and real-time visualization.

🌟 Key Features

• 1D and 2D Simulations:
  • 1D: Temporal evolution of a wave packet in an infinite box.
  • 2D: Visualization as a heatmap (2D) or 3D surface.
• Numerical Method:
  • Crank-Nicolson algorithm for stable time integration.
  • Efficient handling with LU factorization of sparse matrices.
• Interactivity:
  • Buttons to pause, resume, and reset simulations.
  • Intuitive color-supported selection menu.
• Customization:
  • Adjustable physical parameters (length, mass, potential).
  • Configuration of initial conditions (Gaussian packet width, initial momentum).

📦 Prerequisites

• Python 3.8+
• Required libraries:

  pip install numpy matplotlib scipy colorama

🛠️ Installation and Execution

1. Clone the repository:

   git clone https://github.com/your-username/schrodinger-simulator.git
   cd schrodinger-simulator

2. Run the selector:

   python selector.py

🖥️ Simulator Usage

Main Menu

Select an option:

• 1: 1D simulation (probability density plot).
• 2: 2D simulation (2D heatmap visualization).
• 3: 2D simulation (interactive 3D surface).
• q: Exit the program.

Simulation Controls

• Pause/Resume: Freeze or resume temporal evolution.
• Reset: Restore the wave function to its initial state.
• 3D Visualization: Interactive graph rotation (drag with mouse).

📂 Project Structure

schrodinger-simulator/
├── ecuacion1D.py          # 1D simulation with interactive buttons
├── ecuacion2d.py          # 2D simulation (heatmap)
├── ecuacion2d_3d.py       # 2D simulation (3D surface)
├── selector.py            # Interactive selection menu
└── README.md

⚙️ Adjustable Parameters

In the .py files:

• L: Length of the quantum box.
• N: Number of points in the spatial grid.
• dt: Time step (adjust for numerical stability).
• sigma: Initial Gaussian packet width.
• k0: Initial momentum of the wave packet.

📸 Demonstration Screenshots

1D Simulation	2D Simulation (2D)	2D Simulation (3D)

📄 License

This project is licensed under the MIT License. See the LICENSE file for details.