Category: Perturbation theory

Laplace's method
In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form where is a twice-differentiable function, M is a large number, and the endp
Saddlepoint approximation method
The saddlepoint approximation method, initially proposed by Daniels (1954) is a specific example of the mathematical saddlepoint technique applied to statistics. It provides a highly accurate approxim
Perturbation problem beyond all orders
In mathematics, perturbation theory works typically by expanding unknown quantity in a power series in a small parameter. However, in a perturbation problem beyond all orders, all coefficients of the
Order of approximation
In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is.
Series acceleration
In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numeri
Singular perturbation
In mathematics, a singular perturbation problem is a problem containing a small parameter that cannot be approximated by setting the parameter value to zero. More precisely, the solution cannot be uni
In mathematics and physics, a non-perturbative function or process is one that cannot be described by perturbation theory. An example is the function which does not have a Taylor series at x = 0. Ever
Ritz method
The Ritz method is a direct method to find an approximate solution for boundary value problems. The method is named after Walther Ritz, and is also commonly called the Rayleigh–Ritz method and the Rit
Statistical associating fluid theory
Statistical associating fluid theory (SAFT) is a chemical theory, based on perturbation theory, that uses statistical thermodynamics to explain how complex fluids and fluid mixtures form associations
Intruder state
In quantum and theoretical chemistry, an intruder state is a particular situation arising in perturbative evaluations, where the energy of the perturbers is comparable in magnitude to the energy assoc
Sequence transformation
In mathematics, a sequence transformation is an operator acting on a given space of sequences (a sequence space). Sequence transformations include linear mappings such as convolution with another sequ
Fermi's golden rule
In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of ene
Variational perturbation theory
In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say , into a convergent series in powers , where is a c
Method of steepest descent
In mathematics, the method of steepest descent or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms a contour integral in the complex plane to pa
Poincaré–Lindstedt method
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 pertur
Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The ide
Schwinger's quantum action principle
The Schwinger's quantum action principle is a variational approach to quantum mechanics and quantum field theory. This theory was introduced by Julian Schwinger in a series of articles starting 1950.
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. A cri
Multiple-scale analysis
In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation p
Stationary phase approximation
In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to the limit as . This method originates from the 19th century, and is due to George Gabriel St
Tikhonov's theorem (dynamical systems)
In applied mathematics, Tikhonov's theorem on dynamical systems is a result on stability of solutions of systems of differential equations. It has applications to chemical kinetics. The theorem is nam
Matrix element (physics)
In physics, particularly in quantum perturbation theory, the matrix element refers to the linear operator of a modified Hamiltonian using Dirac notation. The matrix element considers the effect of the