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Perturbation theory develops an expression for the desired solution in terms of a formal power series known as a perturbation series in some "small" parameter, that quantifies the deviation from the exactly solvable problem. The leading term in this power series is the solution of the exactly solvable problem, while further terms describe the ...
In astronomy, perturbation is the complex motion of a massive body subjected to forces other than the gravitational attraction of a single other massive body. [1] The other forces can include a third (fourth, fifth, etc.) body, resistance , as from an atmosphere , and the off-center attraction of an oblate or otherwise misshapen body.
Perturbation or perturb may refer to: Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly; Perturbation (geology), changes in the nature of alluvial deposits over time; Perturbation (astronomy), alterations to an object's orbit (e.g., caused by gravitational interactions with other ...
Perturbation theory is an important tool for describing real quantum systems, as it turns out to be very difficult to find exact solutions to the Schrödinger equation for Hamiltonians of even moderate complexity.
The gauge-invariant perturbation theory is based on developments by Bardeen (1980), [7] Kodama and Sasaki (1984) [8] building on the work of Lifshitz (1946). [9] This is the standard approach to perturbation theory of general relativity for cosmology. [10]
In perturbation theory, the Poincaré–Lindstedt method or Lindstedt–Poincaré method is a technique for uniformly approximating periodic solutions to ordinary differential equations, when regular perturbation approaches fail.
Møller–Plesset perturbation theory (MP) is one of several quantum chemistry post-Hartree–Fock ab initio methods in the field of computational chemistry.It improves on the Hartree–Fock method by adding electron correlation effects by means of Rayleigh–Schrödinger perturbation theory (RS-PT), usually to second (MP2), third (MP3) or fourth (MP4) order.
Note that the "perturbation" term ′ gets progressively smaller as k approaches zero. Therefore, k·p perturbation theory is most accurate for small values of k . However, if enough terms are included in the perturbative expansion , then the theory can in fact be reasonably accurate for any value of k in the entire Brillouin zone .