1146
eng
reportzib
0
2009-09-22
2009-09-22
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Computing expectation values for molecular quantum dynamics
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.
09-30
1438-0064
1195
urn:nbn:de:0297-zib-11461
/10.1137/090770461
Appeared in: SIAM J. Sci. Comput. 2010, 32(3), pp. 1465-1483
Caroline Lasser
unknown unknown
Susanna Röblitz
ZIB-Report
09-30
eng
uncontrolled
time dependent Schrödinger equation
eng
uncontrolled
molecular quantum dynamics
eng
uncontrolled
expectation values
eng
uncontrolled
Wigner functions
Mathematik
Numerical integration
Applications to physics
Computational methods
Semiclassical techniques, including WKB and Maslov methods
Phase-space methods including Wigner distributions, etc.
Numerical Mathematics
Röblitz, Susanna
https://opus4.kobv.de/opus4-zib/files/1146/ZR_09_30.pdf