The principal motivation for quasiparticles is that it is almost impossible to directly describe every particle in a macroscopic system. For example, a barely-visible (0.1mm) grain of sand contains around 10 nuclei and 10 electrons. Each of these attracts or repels every other by Coulomb's law. In principle, the Schrödinger equation predicts exactly how this system will behave. But the Schrödinger equation in this case is a partial differential equation (PDE) on a 3×10 -dimensional vector space—one dimension for each coordinate (x, y, z) of each particle. Directly and straightforwardly trying to solve such a PDE is impossible in practice. Solving a PDE on a 2-dimensional space is typically much harder than solving a PDE on a 1-dimensional space (whether analytically or numerically); solving a PDE on a 3-dimensional space is significantly harder still; and thus solving a PDE on a 3×10 -dimensional space is quite impossible by straightforward methods.