Has Computer Simulation Proven Successful in Solving Quantum Mechanical Systems?

[jostpuur]

I've heard stories about how computer simulations can be used to deal with some quantum mechanical systems, that cannot be solved exactly (for example systems with 10, 20, or 100 interacting particles) even though the number of particles is small enough that some explicit solutions do exist in principle. However, it has not become clear to me how successful these techniques have been. For example, have the spectrum of some heavier atoms, or some molecules, been solved correctly purely from the theory?

 

[DrClaude]

All modelling is based on approximations, and the results are limited by the quality and applicability of these approximations, but some very good calculations have been made.

Note that for heavier atoms, the difficulty stems not only from the number of particles involved, but also from the fact that relativistic effects have to be taken into account. But there also, some good work has been done.