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I have a code which simulates the Schrodinger equation and it works good for the harmonic potential, I have checked that. Now, i have changed the Hamiltonian, I have the results but I want to compare them with a good working simulation result to know if my simulation is correct. Is there something like that?

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Use your code to find solutions to the finite square well potential or the radial eigenstates of the Hydrogen atom. Compare the energies of your eigenstates to the real solutions.

You can check out the PhET simulations for common quantum-mechanical systems: https://phet.colorado.edu/en/simulations/category/physics/quantum-phenomena

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