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High‐Order Time‐Dependent Perturbation Theory for Classical Mechanics and for Other Systems of First‐Order Ordinary Differential Equations

Marcus, R. A. (1970) High‐Order Time‐Dependent Perturbation Theory for Classical Mechanics and for Other Systems of First‐Order Ordinary Differential Equations. Journal of Chemical Physics, 52 (9). pp. 4803-4807. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:20120802-085756570

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Abstract

A time‐dependent perturbation solution is derived for a system of first‐order nonlinear or linear ordinary differential equations. By means of an ansatz, justified a posteriori, the latter equations can be converted to an operator equation which is solvable by several methods. The solution is subsequently specialized to the case of classical mechanics. For the particular case of autonomous equations the solution reduces to a well‐known one in the literature. However, when collision phenomena are treated and described in a classical “interaction representation” the differential equations are typically nonautonomous, and the more general solution is required. The perturbation expression is related to a quantum mechanical one and will be applied subsequently to semiclassical and classical treatments of collisions.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.1673715 DOIUNSPECIFIED
http://jcp.aip.org/resource/1/jcpsa6/v52/i9/p4803_s1PublisherUNSPECIFIED
Additional Information:© 1970 American Institute of Physics. Received 24 November 1969. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. This research was also supported by a grant from the National Science Foundation at the University of Illinois.
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American Chemical Society Petroleum Research FundUNSPECIFIED
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Record Number:CaltechAUTHORS:20120802-085756570
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120802-085756570
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32866
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Aug 2012 16:12
Last Modified:26 Dec 2012 15:47

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