varistusmenetelmä

Varistusmenetelmä, often translated as "variation method" or "perturbation method" in English, is a technique used in physics and mathematics to find approximate solutions to complex problems that cannot be solved exactly. It is particularly useful when a problem can be expressed as a small deviation from a simpler, solvable problem. The core idea is to start with the known solution to the simpler problem and then systematically introduce corrections to account for the added complexity.

The method typically involves defining a small parameter, often denoted by epsilon (ε), that represents the magnitude of the difference between the exact problem and the solvable approximation. The solution to the complex problem is then expressed as a power series in this parameter: the solution is a sum of terms, where the first term is the exact solution to the simpler problem, and subsequent terms represent increasingly refined corrections. Each correction term is determined by substituting this series into the original equation and equating coefficients of corresponding powers of ε.

The varistusmenetelmä is widely applied in quantum mechanics, where it is used to calculate the energy levels and wave functions of atoms and molecules under the influence of external fields or when considering electron-electron interactions. It also finds application in fluid dynamics, celestial mechanics, and other areas of science and engineering where analytical solutions are elusive. The accuracy of the approximation depends on the smallness of the parameter ε and the number of correction terms included in the series. If ε is sufficiently small, the first few terms of the series can provide a very good approximation.