This is a MATLAB tool for solving numerically the highly oscillatory 1D Schrödinger equation
Here, a(x) is a real valued coefficient function bounded away from zero and epsi is the rescaled Planck constant 0 < epsi << 1.
The whole program directly corresponds to the article: A. Arnold, J. Körner: "WKB-based third order method for the highly oscillatory 1D stationary Schrödinger equation" [(https://doi.org/10.1007/s10444-025-10234-y)].
The main program is "third_order_WKB_marching_method.m".
To run the program the following requirements are needed:
- MATLAB
Just clone the repository
git clone https://github.com/JannisKoerner/third-order-WKB-marching-method.gitor download it manually.
Make sure the folder is added to the MATLAB search path.
For a quick start you can just run the example file "Test_third_order_WKB_marching_method_Airy.m". A plot of the numerical solution is created together with the corresponding reference solution, as well as a plot of the relative error over the specified spatial interval:
Notice that although the true solution becomes increasingly oscillatory, the error of the numerical solution does not increase, even though a constant grid size is used.
There are short documentations available, just type the following commands into your MATLAB console:
doc third_order_WKB_marching_methodThis work is licensed under a Creative Commons Attribution 4.0 International License.
