Fast Gaussian wavepacket transforms and Gaussian beams for the Schroedinger equation
This paper introduces a wavepacket-transform-based Gaussian beam method for solving the Schroedinger equation. We focus on addressing two computational issues of the Gaussian beam method: how to generate a Gaussian beam representation for general initial conditions and how to perform long time propa...
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| Veröffentlicht in: | Journal of computational physics 2010-10, Vol.229 (20), p.7848-7873 |
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| container_title | Journal of computational physics |
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| creator | Qian, Jianliang Ying, Lexing |
| description | This paper introduces a wavepacket-transform-based Gaussian beam method for solving the Schroedinger equation. We focus on addressing two computational issues of the Gaussian beam method: how to generate a Gaussian beam representation for general initial conditions and how to perform long time propagation for any finite period of time. To address the first question, we introduce fast Gaussian wavepacket transforms and develop on top of them an efficient initialization algorithm for general initial conditions. Based on this new initialization algorithm, we address the second question by reinitializing the beam representation when the beams become too wide. Numerical examples in one, two, and three dimensions demonstrate the efficiency and accuracy of the proposed algorithms. The methodology can be readily generalized to deal with other semi-classical quantum mechanical problems. |
| doi_str_mv | 10.1016/j.jcp.2010.06.043 |
| format | Article |
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We focus on addressing two computational issues of the Gaussian beam method: how to generate a Gaussian beam representation for general initial conditions and how to perform long time propagation for any finite period of time. To address the first question, we introduce fast Gaussian wavepacket transforms and develop on top of them an efficient initialization algorithm for general initial conditions. Based on this new initialization algorithm, we address the second question by reinitializing the beam representation when the beams become too wide. Numerical examples in one, two, and three dimensions demonstrate the efficiency and accuracy of the proposed algorithms. 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The methodology can be readily generalized to deal with other semi-classical quantum mechanical problems.</description><subject>ACCURACY</subject><subject>ALGORITHMS</subject><subject>Beams (radiation)</subject><subject>DIFFERENTIAL EQUATIONS</subject><subject>EFFICIENCY</subject><subject>EQUATIONS</subject><subject>Gaussian</subject><subject>Gaussian beams (optics)</subject><subject>Initial conditions</subject><subject>MATHEMATICAL LOGIC</subject><subject>MATHEMATICAL METHODS AND COMPUTING</subject><subject>Mathematical models</subject><subject>MECHANICS</subject><subject>PARTIAL DIFFERENTIAL EQUATIONS</subject><subject>QUANTUM MECHANICS</subject><subject>Representations</subject><subject>SCHROEDINGER EQUATION</subject><subject>TRANSFORMATIONS</subject><subject>Transforms</subject><subject>WAVE EQUATIONS</subject><subject>WAVE PACKETS</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNpFjsFOwzAQRC0EEqXwAdwsceCUsOu4iXNEFRSkShzoPdo4G5rS2m3swO-TUiROo5l92hkhbhFSBMwfNunG7lMFo4c8BZ2diQlCCYkqMD8XEwCFSVmWeCmuQtgAgJlpMxGrZwpRLmgIoSMnv-mL92Q_OcrYkwut73dBkmv-kZppjMaDjGuW73bde24698G95MNAsfPuWly0tA1886fTseZpNX9Jlm-L1_njMvE5_C5rCua2NKapayhQWYIMLKq6zrSGBrVuW6am5KJs1WhUDmOQAxqVkcmm4u701ofYVcF2ke3aeufYxkqhRoNwpO5P1L73h4FDrHZdsLzdkmM_hKowhTJ6ZiD7AcgsYSg</recordid><startdate>20101001</startdate><enddate>20101001</enddate><creator>Qian, Jianliang</creator><creator>Ying, Lexing</creator><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>OTOTI</scope></search><sort><creationdate>20101001</creationdate><title>Fast Gaussian wavepacket transforms and Gaussian beams for the Schroedinger equation</title><author>Qian, Jianliang ; Ying, Lexing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-o600-271d7eef988dbb0712ca030c12bb3440d144ffead9e79f244f260ffe601823a83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>ACCURACY</topic><topic>ALGORITHMS</topic><topic>Beams (radiation)</topic><topic>DIFFERENTIAL EQUATIONS</topic><topic>EFFICIENCY</topic><topic>EQUATIONS</topic><topic>Gaussian</topic><topic>Gaussian beams (optics)</topic><topic>Initial conditions</topic><topic>MATHEMATICAL LOGIC</topic><topic>MATHEMATICAL METHODS AND COMPUTING</topic><topic>Mathematical models</topic><topic>MECHANICS</topic><topic>PARTIAL DIFFERENTIAL EQUATIONS</topic><topic>QUANTUM MECHANICS</topic><topic>Representations</topic><topic>SCHROEDINGER EQUATION</topic><topic>TRANSFORMATIONS</topic><topic>Transforms</topic><topic>WAVE EQUATIONS</topic><topic>WAVE PACKETS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qian, Jianliang</creatorcontrib><creatorcontrib>Ying, Lexing</creatorcontrib><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>OSTI.GOV</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qian, Jianliang</au><au>Ying, Lexing</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fast Gaussian wavepacket transforms and Gaussian beams for the Schroedinger equation</atitle><jtitle>Journal of computational physics</jtitle><date>2010-10-01</date><risdate>2010</risdate><volume>229</volume><issue>20</issue><spage>7848</spage><epage>7873</epage><pages>7848-7873</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>This paper introduces a wavepacket-transform-based Gaussian beam method for solving the Schroedinger equation. 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| fulltext | fulltext |
| identifier | ISSN: 0021-9991 |
| ispartof | Journal of computational physics, 2010-10, Vol.229 (20), p.7848-7873 |
| issn | 0021-9991 1090-2716 |
| language | eng |
| recordid | cdi_osti_scitechconnect_21418108 |
| source | Elsevier ScienceDirect Journals Complete |
| subjects | ACCURACY ALGORITHMS Beams (radiation) DIFFERENTIAL EQUATIONS EFFICIENCY EQUATIONS Gaussian Gaussian beams (optics) Initial conditions MATHEMATICAL LOGIC MATHEMATICAL METHODS AND COMPUTING Mathematical models MECHANICS PARTIAL DIFFERENTIAL EQUATIONS QUANTUM MECHANICS Representations SCHROEDINGER EQUATION TRANSFORMATIONS Transforms WAVE EQUATIONS WAVE PACKETS |
| title | Fast Gaussian wavepacket transforms and Gaussian beams for the Schroedinger equation |
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