Quantum Mechanics and Schrodinger Equation Solvers in Python.
The starting point for these calculations is the notebook "Solving_the_Schrodinger_Equation_Numerically.ipynb". In this notebook you will find an explanation on how to setup the Hamiltonian for an infinite square well. It is very easy to change this to any shape potential, bounded on some domain [xlow,xhigh].
An example usage of this way of solving the Schrodinger equation in this way can be found in Harmonic Oscillator.ipynb, which shows how a harmonic state of the H.O. evolves over time. This problem is exactly solvable using the algebra of ladder operators, and agrees with the numerical solution here. You can play some games with this notebook, for example by adding a spike in the center of the well.
A different solution, solving the Time Dependent Schrodinger Equation directly is found in TimePropagation_of_WF.ipynb. This still uses the Hamiltonian, but now solves the time dependence directly, stepping in time. This makes for good solutions to scattering problems.