Ainsleigh Hill
Gowrisankar Sreeram
There are only a few isolated cases where the Schrödinger equation is readily solvable through analytical methods. In such cases, one must use perturbative or numerical methods to approximate a solution to the equation. To this end, we wanted to test a variety of numerical methods on known cases (the infinite square well and the Hydrogen atom) so that we could determine which numerical methods are best suited for these problems.
In our project, we investigated 4 different methods:
- Infinite Square Well: Finite Difference Method
- Hydrogen Atom: Numerov Method
- Hydrogen Atom: Linear Regression with Gradient Descent
- Hydrogen Atom: Variational Method with Gradient Descent