Schrodinger giving ‘the fundamental equation’ for quantum systems was a giant achievement, yet the systems on which it applies are exceedingly complicated to be tackled via analytical methods or even computational methods ‘directly’. Take for instance the Hydrogen atom problem, simplest case in nature, has an analytical solution but is still quite complicated to its merit. Add in a couple more electrons and nuclei, and the equations become almost impossible to solve… this i think paves the way for exploring other methods to find our answers!