Marcus, R. A. (1964) Separation of Sets of Variables in Quantum Mechanics. Journal of Chemical Physics, 41 (3). pp. 603-609. ISSN 0021-9606. doi:10.1063/1.1725934. https://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.
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| 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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| Issue or Number: | 3 | |||||||||
| DOI: | 10.1063/1.1725934 | |||||||||
| Record Number: | CaltechAUTHORS:20120829-110758360 | |||||||||
| Persistent URL: | https://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: | 09 Nov 2021 21:36 |
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