Perturbation (quantum mechanics)

Article By:

Fradkin, David M. Department of Physics, Wayne State University, Detroit, Michigan.

Last reviewed:August 2020

DOI:https://doi.org/10.1036/1097-8542.501500

An expansion technique useful for solving complicated quantum-mechanical problems in terms of solutions for simple problems. Perturbation theory in quantum mechanics provides an approximation scheme whereby the physical properties of a system, modeled mathematically by a quantum-mechanical description, can be estimated to a required degree of accuracy. Such a scheme is useful because very few problems occurring in quantum mechanics can be solved analytically. Consequently an approximation technique must be employed in order to give an approximate analytic solution or to provide suitable algorithms for a numerical solution. Even for problems which admit an exact analytic solution, the exact solution may be of such mathematical complexity that its physical interpretation is not apparent. For these situations, perturbation techniques are also desirable. Here the discussion of the application of perturbation techniques to quantum mechanics will be limited to the domain of nonrelativistic quantum theory. Applications of a similar but mathematically more intricate nature have also been made in quantum electrodynamics and quantum field theory. See also: Nonrelativistic quantum theory; Quantum electrodynamics; Quantum field theory; Quantum mechanics

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