Solving the equations of quantum mechanics for complicated systems becomes exponentially more difficult with each added particle, making simulations impossible because there simply isn't enough computing power to run the calculations.
Research by Dr. Nancy Makri, Gutgsell Professor of Chemistry and Professor of Physics at the University of Illinois Urbana-Champaign, and Vikram Jadhao, a graduate student in the Department of Physics, University of Illinois at Urbana-Champaign, is outlined in a paper that will be published in the The Journal of Chemical Physics, describing a new theoretical method to approach these equations that might not otherwise be solvable.
The new paper by Makri is available at Iterative Monte Carlo for Quantum Dynamics: http://scitation.aip.org/journals/doc/JCPSA6-ft/vol_129/iss_16/161102_1.html.
For more information on Dr. Makri, please contact her at nancy@makri.scs.uiuc.edu.