{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T16:25:55Z","timestamp":1774974355015,"version":"3.50.1"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p> The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schr\u00f6dinger equation. In this paper, a new semi-discretization in space is obtained by wavepacket operator. In a sense, such semi-discretization is equivalent to the Hagedorn wavepacket method, but this discretization is more intuitive to show the advantages of wavepacket methods. Moreover, we apply the multi-time-step method and the Magnus-expansion to obtain the improved algorithms in time-stepping computation. The improved algorithms are of the Gauss\u2013Hermite spectral accuracy to approximate the analytical solution of the semiclassical Schr\u00f6dinger equation. And for the given accuracy, the larger time stepsize can be used for the higher oscillation in the semiclassical Schr\u00f6dinger equation. The superiority is shown by the error estimation and numerical experiments. <\/jats:p>","DOI":"10.1142\/s1793962314500135","type":"journal-article","created":{"date-parts":[[2014,2,14]],"date-time":"2014-02-14T09:59:10Z","timestamp":1392371950000},"page":"1450013","source":"Crossref","is-referenced-by-count":3,"title":["The improved Hagedorn wavepacket method for semiclassical Schr\u00f6dinger equation"],"prefix":"10.1142","volume":"05","author":[{"given":"Xueyang","family":"Li","sequence":"first","affiliation":[{"name":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan, P. R. China"}]},{"given":"Aiguo","family":"Xiao","sequence":"additional","affiliation":[{"name":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2014,9,29]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-010-1154-0"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492911000031"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050406"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501393253"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01230088"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1006\/aphy.1998.5843"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1137\/080729724"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.4171\/067"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01329203"},{"key":"rf10","first-page":"365","volume":"11","author":"Sun G.","year":"1993","journal-title":"J. Comput. Math."},{"key":"rf11","volume-title":"Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations","author":"Hairer E.","year":"2006"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142995280572"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1063\/1.444328"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drn041"},{"key":"rf15","first-page":"544","volume":"62","author":"Heller E. J.","year":"1975","journal-title":"J. Chem. Phys."}],"container-title":["International Journal of Modeling, Simulation, and Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793962314500135","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T04:05:33Z","timestamp":1565150733000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793962314500135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,29]]},"references-count":15,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2014,9,29]]},"published-print":{"date-parts":[[2014,12]]}},"alternative-id":["10.1142\/S1793962314500135"],"URL":"https:\/\/doi.org\/10.1142\/s1793962314500135","relation":{},"ISSN":["1793-9623","1793-9615"],"issn-type":[{"value":"1793-9623","type":"print"},{"value":"1793-9615","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,29]]}}}