1. Perturbation theory

    In mathematics and physics, perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. Perturbation theory is widely used when the problem at hand does not have a known exact solution, but can be expressed as a "small" change to a known solvable problem. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory for quantum mechanics imparts the first step on this path. The field in general remains actively and heavily researched across multiple disciplines. Wikipedia

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  2. en.wikipedia.org

    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 regular perturbation theory, the solution is expressed as a power ...
  3. phys.libretexts.org

    This method, termed perturbation theory, is the single most important method of solving problems in quantum mechanics, and is widely used in atomic physics, condensed matter and particle physics. It should be noted that there are problems which cannot be solved using perturbation theory, even when the perturbation is very weak, although such ...
  4. phys.uconn.edu

    Learn how to use perturbation theory to obtain approximate solutions to problems involving a small parameter. See examples of regular and singular perturbation problems, and how to apply them to differential equations and boundary-value problems.
  5. Learn how to solve quantum problems with perturbation theory, a method that approximates the solution of a Hamiltonian by expanding it in a small parameter. See the non-degenerate and degenerate cases, the Stark effect, and the time-dependent perturbation theory.
  6. Learn how to use perturbation theory to study the effects of small changes in the Hamiltonian of a quantum system. The web page covers non-degenerate and degenerate perturbation theory, with examples and diagrams.
  7. encyclopediaofmath.org

    A general overview of perturbation theory, a group of methods for studying various problems in mathematics, mechanics, physics, and technology. Learn about the history, applications, and challenges of perturbation theory, such as the problem of small denominators.
  8. chem.libretexts.org

    Jun 30, 2023This method, termed perturbation theory, is the single most important method of solving problems in quantum mechanics and is widely used in atomic physics, condensed matter and particle physics. Perturbation theory is another approach to finding approximate solutions to a problem, by starting from the exact solution of a related, simpler problem.
  9. weichman.princeton.edu

    Learn how to use perturbation theory to solve quantum mechanical problems with small perturbations. The lecture notes cover non-degenerate and degenerate cases, and provide examples of applications to spectroscopy.

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