I need to solve, as mentioned, Schrodinger's equation in a Bunimovich stadium-shaped infinite potential well with Dirichlet BC Numerically (this isn't possible analytically). In order to do so, I need to define the discrete Hamiltonian matrix of the system. Since the shape isn't defined well in any coordinates system, I have no idea how to do so.
Normally (as I did with a square well), I'd define the size of the well and then solve 1D TISE for each dimension using MATLAB eig function. Can it be solved similarly?
Any help will be greatly appreciated.