The Role of Perturbation Theory in the Development of Physics View Full Text


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Chapter Info

DATE

1992

AUTHORS

Martin C. Gutzwiller

ABSTRACT

The mathematical model for classical mechanics has been well understood for some 200 years, while for quantum mechanics it was established in the late 1920’s. Theoretical physics seems to have a threefold task: first to provide the foundations by solving the few problems in mechanics which can be exactly reduced to as many independent mathematical problems as degrees of freedom; second, to validate mechanics by treating dynamical systems where at least two degrees of freedom cannot be separated; third, to extrapolate basic mechanics to systems with infinitely many, non-separable freedoms. The process of validation is almost exclusively based on perturbation theory (PT) whereby the solution to the real problem is seen as a minor modification of an ideal separable problem. The same holds for extrapolation, but with the possibility of relying on global or collective coordinates. PT as a mathematical tool, however, is deceptive: in classical mechanics, it leads to asymptotic series at best, whose accuracy cannot be improved at will; in quantum mechanics, PT does converge occasionally, though not often in the desired range. In either case, its application is limited by the sheer physical labor involved, as higher-order terms are worked out. The historical experience with PT is sketched starting with Newton, and giving some details from celestial mechanics, atomic physics, and quantum electrodynamics. More... »

PAGES

1-18

Book

TITLE

Quantum Chaos — Quantum Measurement

ISBN

978-90-481-4120-3
978-94-015-7979-7

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-015-7979-7_1

DOI

http://dx.doi.org/10.1007/978-94-015-7979-7_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1002040228


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