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Perturbation theory is applicable if the problem at hand cannot be solved exactly, but can be formulated by adding a "small" term to the mathematical description of the exactly solvable problem.
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 ...
Rabi problem in time-dependent perturbation theory [ edit ] In the quantum approach, the periodic driving force can be considered as periodic perturbation and, therefore, the problem can be solved using time-dependent perturbation theory, with
In the approach of classical perturbation theory, we can start with Minkowski vacuum (or another very simple solution, such as the de Sitter lambdavacuum), introduce very small metric perturbations, and retain only terms up to some order in a suitable perturbation expansion—somewhat like evaluating a kind of Taylor series for the geometry of ...
The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear problems with finite oscillatory solutions. [1] [2] The method is named after Henri Poincaré, [3] and Anders Lindstedt. [4]
One place where this occurs is in degenerate perturbation theory, where the off-diagonal elements are nonzero until the problem is solved by diagonalization. Because of the hermiticity of H {\displaystyle \mathbf {H} } the eigenvalues are real; or, rather, conversely, it is the requirement that the energies are real that implies the hermiticity ...
The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Earth, the Moon, and the Sun. [2] In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three ...
This category deals with topics in perturbation theory and variational principles, which commonly occur in the theory of differential equations, with problems in quantum mechanics forming an important subset thereof.