Perturbation theory is a powerful mathematical technique used in various scientific fields such as physics, chemistry, and engineering to find approximate solutions to problems that are too complex to solve exactly. The core idea is to begin with a system that we can solve exactly and then introduce a small disturbance, or _perturbation_, to observe how the behavior of the system changes as a result. To illustrate, imagine a simple system like a swinging pendulum, whose motion we can describe precisely. Now suppose we apply a small external force, such as a gentle breeze. This additional influence slightly alters the pendulum’s motion without completely changing its nature. Perturbation theory allows us to calculate this new motion by treating the breeze as a minor correction to the known system. Mathematically, the new behavior is expressed as a series: the original solution plus a sequence of increasingly smaller corrections, each accounting for the influence of the disturbance. This approach is especially useful in [[Quantum Mechanics|quantum mechanics]], where exact solutions exist only for the simplest systems. A well-known example is the hydrogen [[Atom|atom]]. While we can solve the [[Schrödinger Equation|Schrödinger equation]] exactly for this atom, real-world conditions often introduce complexities such as [[Electric Field|electric]] or [[Magnetic Field|magnetic]] fields, or interactions with additional particles. Perturbation theory enables physicists to model these complexities by calculating how the base solution is altered. In quantum field theory, the technique is indispensable for studying interactions between particles, often visualized through so-called Feynman diagrams. Many predictions in particle physics, including those about [[Electron|electrons]], [[Photon|photons]], and [[Quark|quarks]], depend on perturbative calculations. >[!read]- Further Reading >- [[Classical Physics]] >- [[Quantum Mechanics]] >[!ref]- References