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Homework Statement
I am supposed to write a script that can solve the Schrödinger equation on a nonuniform grid.
Homework Equations
Finite element approximation to the second derivative as in:
https://www.physicsforums.com/threads/nonuniform-finite-element-method.857334/#post-5382329
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?