Comprehensive Poschl-Teller Analysis: Analytic, Harmonic Oscillator Basis, and PINN Solutions

This repository contains a complete and well-documented workflow for solving the one-dimensional Poschl-Teller quantum well using three complementary approaches:

1. Analytic Solutions
   The code computes and visualizes the exact energy eigenvalues and normalized eigenfunctions for the Poschl-Teller potential. It also verifies orthonormality and the diagonal form of the Hamiltonian in the analytic basis.

2. Harmonic Oscillator Basis Expansion
   The Poschl-Teller Hamiltonian is expanded in the basis of harmonic oscillator eigenfunctions. The code checks orthonormality, diagonalizes the Hamiltonian, and compares the numerical eigenstates with analytic results.

3. Physics-Informed Neural Network (PINN) Solution
   A PINN is set up and trained to solve the ground state of the Poschl-Teller well, using both physics and data losses. The results are compared directly to the analytic solution.

The notebook is designed for a clear, step-by-step walkthrough and is suitable for both educational and research purposes.
All integration is performed using Simpson's rule (with appropriate cutoffs for speed and accuracy).

Usage

• Clone this repository
• Open the notebook in Google Colab or Jupyter
• Run each cell in sequence to reproduce the results and plots

Requirements

• Python >= 3.8
• numpy
• matplotlib
• pandas
• scipy
• torch

You can install dependencies with:

pip install numpy matplotlib pandas scipy torch

MIT License

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

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If you use or adapt this code, please cite or link back to this repository and the video.