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Computing expectation values for molecular quantum dynamics

Please always quote using this URN: urn:nbn:de:0297-zib-11461
  • We compute expectation values for the solution of the nuclear Schrödinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to the semiclassical parameter. We present numerical experiments for a two-dimensional torsional potential with three different sets of initial data and for a six-dimensional Henon-Heiles potential. By construction, the computing times scale linearly with the number of initial sampling points and range between three seconds and one hour.

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Author:Caroline Lasser, Susanna RöblitzORCiD
Document Type:ZIB-Report
Tag:Wigner functions; expectation values; molecular quantum dynamics; time dependent Schrödinger equation
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D30 Numerical integration
65-XX NUMERICAL ANALYSIS / 65Zxx Applications to physics / 65Z05 Applications to physics
81-XX QUANTUM THEORY / 81-08 Computational methods
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q20 Semiclassical techniques, including WKB and Maslov methods
81-XX QUANTUM THEORY / 81Sxx General quantum mechanics and problems of quantization / 81S30 Phase-space methods including Wigner distributions, etc.
Date of first Publication:2009/09/22
Series (Serial Number):ZIB-Report (09-30)
Published in:Appeared in: SIAM J. Sci. Comput. 2010, 32(3), pp. 1465-1483
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