The Schrodinger Equation Solver app

This app solves the 2D Schrodinger Equation numerically for arbitrary potential using the finite difference method. Just paste the photo of the infinite potential well.

For the detailed report see

https://www.researchgate.net/publication/340984532_Scars_in_the_wavefunction_A_study_of_different_potential_wells_using_the_finite_difference_method

A YouTube tutorial on how to use the app

https://youtu.be/48cgQMdw94g

How to use the app (summary):

1. Paste the photo of the potential well in the same app file. The photo should be in black and white only. See the example provided. The resolution of the results depends on the resolution of the inputted photo. Start with 30 by 30 pixels photo to see how long the app will take
2. Paste the image name in imagename.txt 3.Select the range of energy values (Results) in energyrange.txt
3. To load the results into python use e_vec = np.load('....npy') e_values = np.load('....npy')

Examples

The heart potential

The stadium billiard

Sinai's billiard

The diamond potential

Also, the app can be used to study the scars in the wavefunction. This is an example,

For more examples, see

https://drive.google.com/drive/folders/1oS9dF2Q94D5c0zO84e2bC_oAiCWi8uA8?usp=sharing

Authors

@main_author: Ahmed Alkharusi

Esah Bannister has participated in writing the code and the report. esah.bannister@student.manchester.ac.uk