Welcome to the repository dedicated to the numerical exploration of the Schrödinger Equation applied to a particle navigating a Double-Well Potential Curve. The project utilizes numerical methods numerical methods to dissect the behaviour of particles in the context of a double-well potential.
- Developed a comprehensive double-well potential model.
- Solved the one-dimensional time-independent Schrödinger equation, initially for a particle resembling an electron and extend it to the complex structure of the ammonia molecule.
- Made judicious assumptions to simplify the problem while retaining essential physical characteristics.
- Derived the governing equations for the one-dimensional Schrödinger equation.
- Formulated initial conditions and boundary conditions necessary for solving the Schrödinger equation for both systems.
- Implemented suitable numerical schemes, including the Finite Difference Method (FDM).
This project was completed in the third semester of the Indian Institute of Technology, Gandhinagar as part of the MA203: Numerical Methods course. Together with four other team members, it was finished in a collaborative manner, adding to the coursework and real-world use of quantum physics numerical methods.