Some note on creating a two-dimensional Schrodinger equation solver with neural network.
As a python beginner, an efficient way to learn programming is to solve something that you are interested in. In my case, solving some physics problem . Schrodinger equation is a basic equation in quantum physics, which describe the wave properties and the energy eigenstates of the particle. Exact solutions of some simple system in low dimensions are well known. After studying [1], a one dimensional Schrodinger equation solver with the neural network, I would like to do the same thing in two dimensions. I will put some codes on Github recently, so keep following for updating information. Start from one-dimensional system, the time-independent Schrodinger equation is: $ -\frac{\hbar^2}{2m} \frac{d^2}{dx^2} \Psi(x) + V(x) \Psi(x) = E \Psi(x) $ we use gradient descent algorithm in TensorFlow to approximate the ground state solution for training data. Slicing space into discrete points, the neural network here contains two hidden layers and 128 ...