The second approach, dealing in coordinate space, provides more flexibility with the hamiltonians it admits, although they can get increasingly difficult to express in code (especially for differential operators, for which symbolic differentiation might be needed). This method is less straightforward, as we actually require integration (which is performed through Hermit-Gaussian Quadrature), and expressing the eigenstates as actual polynomials and functions (rather than simply vectors).

Both methods provide similar results, but coordinate space is much less efficient. Pytorch was used for a standard optimization of the coefficients, but computing the loss was the biggest obstacle.