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  2. Perturbation theory - Wikipedia

    en.wikipedia.org/wiki/Perturbation_theory

    An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields and reaches its most sophisticated and advanced forms in quantum field theory.

  3. Perturbation theory (quantum mechanics) - Wikipedia

    en.wikipedia.org/wiki/Perturbation_theory...

    In practice, convergent perturbation expansions often converge slowly while divergent perturbation expansions sometimes give good results, c.f. the exact solution, at lower order. [ 1 ] In the theory of quantum electrodynamics (QED), in which the electron – photon interaction is treated perturbatively, the calculation of the electron's ...

  4. Singular perturbation - Wikipedia

    en.wikipedia.org/wiki/Singular_perturbation

    Singular perturbation theory is a rich and ongoing area of exploration for mathematicians, physicists, and other researchers. The methods used to tackle problems in this field are many. The more basic of these include the method of matched asymptotic expansions and WKB approximation for spatial problems, and in time, the Poincaré–Lindstedt ...

  5. Poincaré–Lindstedt method - Wikipedia

    en.wikipedia.org/wiki/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 perturbation approaches fail.

  6. Rabi problem - Wikipedia

    en.wikipedia.org/wiki/Rabi_problem

    The classical Rabi problem gives some basic results and a simple to understand picture of the issue, but in order to understand phenomena such as inversion, spontaneous emission, and the Bloch–Siegert shift, a fully quantum-mechanical treatment is necessary.

  7. Multiple-scale analysis - Wikipedia

    en.wikipedia.org/wiki/Multiple-scale_analysis

    As an example for the method of multiple-scale analysis, consider the undamped and unforced Duffing equation: [1] + + =, =, =, which is a second-order ordinary differential equation describing a nonlinear oscillator.

  8. Perturbation function - Wikipedia

    en.wikipedia.org/wiki/Perturbation_function

    In mathematical optimization, the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any such function defines a perturbation of the initial problem.

  9. Fermi's golden rule - Wikipedia

    en.wikipedia.org/wiki/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 energy eigenstates in a continuum, as a result of a weak perturbation.

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