| Determination of Scaling Parameter and Dynamical Resonances in Complex-Rotated Hamiltonian Ⅰ： Theory |
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| 作者姓名： | ZHAO Fang ;ZHAO Mei-Shan |
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| 作者单位： | [1]Department of Mathematics and Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA; [2]The James Pranck Institute and Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA |
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| 基金项目： | Acknowledgments This work is supported in part by a grant from the Collegiate Scholars Program. One of the authors, Fang Zhao, was supported in part by VIGRE （Vertical Integration of Research and Education） at The University of Chicago. |
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| 摘 要： | In this paper we present a theoretical analysis on the determination of the scaling parameter in the complex-rotated Hamiltonian, which has served as a basis for successful applications of the rigged Hilbert space theory for resonances. Based on the complex energy eigenvalue, E（θ） = ER（θ） - iГ（θ）/2, as a function of the scaling parameter θ, we find that for potential barrier scattering, the condition dГ（θI）/dθ = 0 uniquely determines the scaling parameter 8. The condition d ER （θR）/ dθ = 0 is merely a consequence of the Virial theorem and θI =θR is not a necessary condition for a resonance state. We also provide a harmonic approximation formMism for resonances in scattering over a potential barrier.
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| 关 键 词： | 测定方法 标定参数 动力学 共振 哈密顿函数 |
Determination of Scaling Parameter and Dynamical Resonances in Complex-Rotated Hamiltonian Ⅰ： Theory |
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| ZHAO Fang,;ZHAO Mei-Shan.Determination of Scaling Parameter and Dynamical Resonances in Complex-Rotated Hamiltonian Ⅰ： Theory[J].Communications in Theoretical Physics,2008,49(3):599-606. |
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| Authors: | ZHAO Fang ZHAO Mei-Shan |
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| Institution: | [1]Department of Mathematics and Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA [2]The James Pranck Institute and Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA |
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| Abstract: | complex-rotated Hamiltonian, potential scattering resonances, rigged Hilbert space |
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| Keywords: | complex-rotated Hamiltonian potential scattering resonances rigged Hilbert space |
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