The formulation and development of quantum theory in the first half of the century has led to a revolution in our understanding of fundamental physics. Quantum theory has demonstrated a surprising accuracy and predictive power, and the importance of quantum theory in the pure and applied sciences in virtually unchallenged.
The relevant equations to be solved are clearly the equations of quantum mechanics , if we are to attempt to model real processes and real materials. Unfortunately, Schrödinger's equation, the most fundamental equation of wavefunction based quantum mechanics, cannot be solved analytically for all but the most trivial of systems, most of which are not relevant to the world at large.
In order to make useful progress the equations must be solved