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Separation of Sets of Variables in Quantum Mechanics

Marcus, R. A. (1964) Separation of Sets of Variables in Quantum Mechanics. Journal of Chemical Physics, 41 (3). pp. 603-609. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:20120829-110758360

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Abstract

Separation of the Schrödinger equation for molecular dynamics into sets of variables can sometimes be performed when separation into individual variables is neither possible nor for certain purposes necesary. Sufficient conditions for such a separation are derived. They are the same as those found by Stäckel for the corresponding Hamilton—Jacobi problem, with an additional one which is the analog of the Robertson condition for one‐dimensional sets. Expressions are also derived for operators whose eigenvalues are the separation constants. They provide a variational property for these constants. For use in aperiodic problems an expression is obtained for the probability current in curvilinear coordinates in an invariant form. Application of these results to reaction rate theory is made elsewhere.


Item Type:Article
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http://dx.doi.org/10.1063/1.1725934 DOIUNSPECIFIED
http://jcp.aip.org/resource/1/jcpsa6/v41/i3/p603_s1PublisherUNSPECIFIED
Additional Information:© 1964 American Institute of Physics. Received 5 March 1964. Online Publication Date: 2 July 2004. Research performed in part under auspices of the U.S. Atomic Energy Commission. This research was supported in part by a fellowship from the Alfred P. Sloan Foundation.
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Atomic Energy CommissionUNSPECIFIED
Alfred P. Sloan Foundation Fellowship UNSPECIFIED
Record Number:CaltechAUTHORS:20120829-110758360
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120829-110758360
Official Citation:Separation of Sets of Variables in Quantum Mechanics R. A. Marcus J. Chem. Phys. 41, 603 (1964); http://dx.doi.org/10.1063/1.1725934
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33652
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:29 Aug 2012 18:23
Last Modified:26 Dec 2012 16:04

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