Häiritusteooria

Häiritusteooria, or perturbation theory, is a mathematical method used to find approximate solutions to problems that cannot be solved exactly. It is commonly applied in physics and engineering when a system is close to a solvable form but has a small additional term, known as the perturbation. The core idea is to assume that the solution to the complex problem can be expressed as a series expansion of the solution to the simpler, unperturbed problem, plus a series of correction terms that account for the perturbation.

The method starts with a well-understood system (the unperturbed system) for which an exact solution is known. Then, a small change or "perturbation" is introduced to this system. Häiritusteooria assumes that the solution to the perturbed system will be close to the solution of the unperturbed system. The correction terms are calculated sequentially, with each term representing a progressively smaller adjustment to the solution. This allows for an approximation of the true solution by summing the unperturbed solution and the first few correction terms.

This technique is particularly useful in quantum mechanics, celestial mechanics, and fluid dynamics. For instance, in quantum mechanics, it's used to calculate the energy levels and wave functions of atoms and molecules when external fields are present. In celestial mechanics, it helps predict the orbits of planets and satellites, which are constantly influenced by the gravitational pull of other celestial bodies. While häiritusteooria provides approximations, its effectiveness depends on the smallness of the perturbation; the smaller the perturbation, the more accurate the approximation generally is.