Classical physics offers a relatively easy approach to describing how objects move in our everyday world. But in the realm of quantum physics, this task is much more challenging. Determining how a quantum particle behaves requires the use of the wave equation devised by Erwin Schrödinger, which is more difficult to solve than classic mechanical equations.
The situation becomes particularly tricky when studying the behaviour of multiple, interacting objects rather than just a single object. The quantum mechanical equations used to describe these many-particle systems are much more complex than those of single-particle systems, as the complexity increases exponentially with each additional particle. Today's best supercomputers can solve the wave equation for systems with a maximum of 50 particles. And not many more will be possible in the future, since even a supercomputer the size of our planet would not be able to solve Schrödinger's equation accurately for systems much larger than 100 particles.
To read more, click here.