Abstract
Time dependent constants of the motion enable us to treat time evolving states using techniques and points of view made familiar in stationary state problems. This review introduces the concept and main properties of time dependent constants of the motion and surveys their primary applications with special reference to the maximum entropy formalism. The role of time dependent constants in determining what dynamical information is relevant for a particular experimental situation is emphasized. Particular attention is given to the situation where the true Hamiltonian is unknown and experimental input is used to identify the time dependent constants.
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References
Sudarshan, E.C.G. and Mukunda, N., Classical Dynamics (Wiley, N.Y., 1974 ).
Anderson, R.L., Kumei, S. and Wulfman, C.E.; 1972, Rev. Fiz. Mexicana 21, 1;
Aronson, E.B., Malkin, I.A. and Man’ko, V.I.: 1974, Sov. J. Particles Nucl. 5, 47.
Dothan, J.: 1970, Phys. Rev. D2, 2944.
Levine, R.D.: 1981, Adv. Chem. Phys. 47, 239.
Levine, R.D. and Wulfman, C.E.: 1982, Chem. Phys. Letts. 87, 105.
Pfeifer, P. and Levine, R.D.: Phys. Rev. A, in press.
Levine, R.D.: 1981, Chem. Phys. Letts. 79, 205.
Lewis, H.R. and Riesenfeld, J.: 1969, Math. Phys. 10, 1458;
Malkin, I.A., Man’ko, V.I. and Trifonov, D.A.: 1973, J. Math. Phys. 14, 576.
Alhassid, Y. and Levine, R.D.: 1977, J. Chem. Phys. 67, 4321.
Alhassid, Y. and Levine, R.D.: 1978, Phys. Rev. A 18, 89.
Alhassid, Y. and Levine, R.D.: 1979, Phys. Rev. C 20, 1775.
Levine, R.D. and Wulfman, C.E.: 1979, Chem. Phys. Letts. 60, 372.
Levine, R.D. in Intramolecular Dynamics (Reidel, Dordrecht, 1982 ) p. 17.
Levit, S.: 1980, Phys. Rev. C 21, 1594;
Alhassid, Y. and Koonin, S.E.: 1981, Phys. Rev. C 23, 1590.
Wulfman, C.E. and Levine, R.D.: 1981, Chem. Phys. Letts. 84, 13.
Anderson, R.L., Shibuya, T. and Wulfman, C.E.: 1974, Rev. Fiz. Mexicana 2 3, 257.
Levine, R.D. in The Maximum Entropy Formalism (M.I.T. Press, Cambridge, 1979 ).
Levine, R.D. and Bernstein, R.B., Molecular Reaction Dynamics ( Clarendon Press, Oxford, 1974 ).
Iachello, F. and Levine, R.D.: Chem. Phys., in press.
Levine, R.D.: 1978, Ann. Rev. Phys. Chem. 29, 59.
Alhassid, Y., Levine, R.D., Karp, J.S. and Steadman, S.G.: 1979, Phys. Rev. C 20, 1789.
Levine, R.D. and Ungar, T.: Phys. Rev. Lett., in press.
Ruelie, D., Statistical Mechanics (Benjamin, N.Y., 1969 );
Falk, H.: 1970, Am. J. Phys. 38, 858.
Levine, R.D., Quantum Mechanics of Molecular Rate Processes (Oxford University Press, 1969 ), Sec. 3. 5. 1.
Pfeifer, P. and Levine, R.D.: J. Chem. Phys., in press.
Brenner, J.L., quoted by F.T. Smith in Kinetic Processes in Gases and Plasmas (Academic Press, N.Y., 1969 ).
Thirring, W., A Course in Mathematical Physics (Springer Verlag, Berlin, 1980 ), V. 3.
Primas, H.: 1963, Rev. Mod. Phys. 35, 710.
Kubo, R.: 1957, J. Phys. Soc. Japan 12, 570.
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© 1983 D. Reidel Publishing Company
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Levine, R.D. (1983). Time Dependent Constants of the Motion. In: Löwdin, PO., Pullman, B. (eds) New Horizons of Quantum Chemistry. International Academy of Quantum Molecular Science, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7950-5_12
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DOI: https://doi.org/10.1007/978-94-009-7950-5_12
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