Perturbationsteoriat

Perturbationsteoriat, often translated as perturbation theory, is a mathematical method used to find approximate solutions to problems that cannot be solved exactly. It is particularly useful in physics and engineering when dealing with complex systems that can be broken down into a simpler solvable part and a small, manageable "perturbation". The core idea is to start with the known solution of the simpler system and then iteratively improve it by accounting for the effects of the perturbation.

The method involves expanding the solution in terms of a small parameter, often denoted by a Greek letter such as epsilon (ε), which represents the strength of the perturbation. This expansion is typically a power series. The first term in the series is the solution to the unperturbed system. Subsequent terms correct this solution by incorporating the influence of the perturbation. Each successive term in the series is usually smaller than the previous one, allowing for an approximation by truncating the series after a certain number of terms.

Perturbation theory finds widespread application. In quantum mechanics, it is used to calculate the energy shifts and wave function modifications of atoms and molecules when subjected to external fields or when considering interactions between particles. In celestial mechanics, it helps in understanding the long-term evolution of planetary orbits, which are perturbed by the gravitational influence of other celestial bodies. Fluid dynamics and electromagnetism also employ perturbation theory to analyze phenomena like the flow of slightly viscous fluids or the behavior of electromagnetic waves in complex media. The validity of the approximation depends crucially on the perturbation being sufficiently small.