I have been studying Perturbation theory in my Quantum class but my professor has not really explained why physically it comes into play. The book says that perturbation theory is used to help come up with approximate solutions to the Schrodinger Equation. Is this analagous to how we use Fourier series to express solutions to partial differential equations as infinite series? Only instead of using an infinite number of terms, we take the first few for an approximation ? Is there any physical significance or is perturbation theory just pure mathematics?