Having read the quantum physics sequence I am interested in simulating particles at the level of quantum mechanics (for my own experimentation and education). While the sequence didn't go into much technical detail, it seems that the state of a quantum system comprises an amplitude distribution in configuration space for each type of particle, and that the dynamics of the system are governed by the Shroedinger equation. The usual way to simulate something like this would be to approximate the particle fields as piecewise linear and update iteratively according to the Shroedinger equation. Some questions:

• Does anyone have a good source for the technical background I will need to implement such a simulation? Specifically more technical details of the Shroedinger equation (the wikipedia article is unhelpful)

• I imagine this will quickly become intractable quite as I try to simulate more complex systems with more particles. How quickly, though? Could I simulate, e.g., the interaction of two H_2 ions in a reasonable time (say, no more than a few hours)?

• Surely others have tried this. Any links/references would be much appreciated.