1. The problem statement, all variables and given/known data I am supposed to write a script that can solve the Schrödinger equation on a nonuniform grid. 2. Relevant equations Finite element approximation to the second derivative as in: https://www.physicsforums.com/threads/nonuniform-finite-element-method.857334/#post-5382329 3. The attempt at a solution I have defined a grid x = [x1,x2,x3,....,x4] with nonuniform spacing and a potential V(x). Specifically the nonuniform spacing is such that the first 10 points have a spacing of 10-10 and the others have 10-9. I have then solved the Schrödinger equation by finding eigenvectors of: H = -ħ2/2m D + V The problem is that these have some kind of weird oscillatory behaviour, which stems from the discontinuity in the distance between the grid points. Do anyone have an idea what I could be doing wrong?