A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials
文献类型：期刊论文
| 作者 | Wen, Xin |
| 刊名 | JOURNAL OF SCIENTIFIC COMPUTING
 |
| 出版日期 | 2010-02-01 |
| 卷号 | 42期号:2页码:318-344 |
| 关键词 | Semiclassical limit Schrodinger equation Liouville equation Discontinuous potential |
| ISSN号 | 0885-7474 |
| DOI | 10.1007/s10915-009-9326-9 |
| 英文摘要 | We develop a fourth order numerical method for the computation of multivalued physical observables (density, momentum, etc.) in the semiclassical limit of the one-dimensional linear Schrodinger equation in the case of discontinuous potentials. We adopt the level set framework developed in (Jin et al. in J. Comput. Phys. 210:497-518, 2005) which allows one to compute the multivalued physical observables via solving the classical Liouville equation with bounded initial data and approximating delta function integrals. We achieve high order accuracy for our method by studying two issues. The first is to highly accurately compute the solution and its derivatives of the Liouville equation with bounded initial data and discontinuous potentials. The second is to design high order numerical methods to evaluate one-dimensional delta function integrals with discontinuous kernel functions. Numerical examples are presented to verify that our method achieves the fourth order L (1)-norm accuracy for computing multivalued physical observables of the one-dimensional linear Schrodinger equation with general discontinuous potentials. |
| 语种 | 英语 |
| WOS记录号 | WOS:000273452600007 |
| 出版者 | SPRINGER/PLENUM PUBLISHERS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/10783]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Wen, Xin |
| 作者单位 | Chinese Acad Sci, LSEC, Inst Computat Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Wen, Xin. A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials[J]. JOURNAL OF SCIENTIFIC COMPUTING,2010,42(2):318-344. |
| APA | Wen, Xin.(2010).A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials.JOURNAL OF SCIENTIFIC COMPUTING,42(2),318-344. |
| MLA | Wen, Xin."A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrodinger Equation with Discontinuous Potentials".JOURNAL OF SCIENTIFIC COMPUTING 42.2(2010):318-344. |
入库方式： OAI收割
来源：数学与系统科学研究院
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