PERTURBATION THEORY Meaning and
Definition
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Perturbation theory is a mathematical technique used to approximate solutions to complex problems in physics and other scientific disciplines. It is particularly useful when dealing with systems that are difficult to solve exactly, allowing for a systematic approximation of the behavior of these systems.
In essence, perturbation theory is based on the concept of a perturbation, which refers to a small change or disturbance introduced into a system. By breaking down a complex system into a simpler one, perturbation theory allows researchers to analyze the effects of the perturbation and obtain approximate solutions or make predictions about the system's behavior.
The approach involves expanding the equations that describe the system's behavior as a series of terms, known as perturbation series. The series typically starts with the equations for the unperturbed system, which can be solved exactly, and then incorporates successive terms representing the effects of the perturbation. Each term in the series represents a higher-order correction to the system's behavior, hence providing progressively more accurate approximations.
Perturbation theory is heavily employed in quantum mechanics, where it allows researchers to tackle problems involving the interaction of particles or the behavior of atoms and molecules. It is also used in celestial mechanics, fluid dynamics, and many other fields of science and engineering where complex systems are encountered.
Etymology of PERTURBATION THEORY
The word "perturbation theory" has its origins in the Latin word "perturbare", which means to disturb or disrupt. The term "perturbation" refers to a disturbance or deviation from a normal state or condition. In physics and mathematics, perturbation theory is a method used to solve problems that involve small deviations or disturbances from an idealized or simplified system. It was first introduced by mathematician Pierre-Simon Laplace in the late 18th century to analyze the effects of small perturbations on celestial bodies within the framework of Newtonian mechanics. The term "perturbation theory" has since been widely used to describe similar methods across various disciplines.
