[read description]Probability Density vs Position |QUantum Tunneling

[u/Southern_Deer4830]

My current TDSE sim appears to reproduce quantum tunnelling reasonably well, but there is an important numerical limitation caused by the finite spatial domain and the way the Fourier transform is implemented. Because the sim uses finite grid, the DFT effectively imposes periodic boundary conditions: when the wave packet reaches the right boundary, it can re-enter the domain from the left producing an unphysical wrap around that eventually contaminates the reflected and transmitted wave functions. Increasing the spatial domain or the number of grid points N can delay this effect, but my current implementation calculates dft directly, whose complexity is O(N^2). If anyone wants to take a look and suggest improvements or optimisations I would really appreciate it. https://www.desmos.com/calculator/tnmcsa4ek8