Perturbation Theory

In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.[1][2] A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts.[3] In perturbation theory, the solution is expressed as a power series in a small parameter ε {\displaystyle \varepsilon } .[1][2] The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of ε {\displaystyle \varepsilon } usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction.