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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 趙聖德(SHENG-DER CHAO) | |
| dc.contributor.author | I-Huan Wu | en |
| dc.contributor.author | 吳宜洹 | zh_TW |
| dc.date.accessioned | 2021-06-17T06:02:04Z | - |
| dc.date.available | 2024-02-13 | |
| dc.date.copyright | 2019-02-13 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-01-30 | |
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Journal of mathematical physics, 26(12), 3105-3108. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/71506 | - |
| dc.description.abstract | 本文延伸本實驗室發展的一個創新且有系統的方法－動能分離法(Kinetic Energy Partition)，用於求解量子力學中特徵值問題。其中利用動能項中質量的拆解，將拆解後的動能項分別與對應的位能項形成子系統，將總漢米爾頓系統拆解為多個子系統之和。首先從最簡單的單體問題，逐漸增加複雜度包含粒子數、維度以及交互作用模式來討論。其中在多電子系統中，使用“負質量”的觀念，來處理斥力位能的部分，使其能量有束縛解，以降低具有連續能增的基底函數的數目。以及在多體系統中，為了化簡動能分離法的過程，使用絕熱近似法(Adiabatic Approximation)將動能分離法作近似。本研究使用摩辛斯基原子及虎克原子和狄拉克原子等模型來檢視動能分離法的可行性，其誤差大致在5%以內的精準度。並且首次使用動能分離法挑戰三體問題，使用一維摩辛斯基原子以證明此方法是有機會推廣至多體問題。此外另一個研究部分是變分的動能分離法(Variational KEP)，將探討動能分離法的理論基礎，研究其和變分法的關係。因為動能分離法的一個特點是能夠引入新的變分參數，我們相信變分的動能分離法能夠改進原來的動能分離法，使它達到更高準確度，並使用最簡單的例子是雙負狄拉克函數位能來驗證其可行性。 | zh_TW |
| dc.description.abstract | This study extends a novel and systematic scheme, kinetic energy partition (KEP) method, developed by our group for solving the general quantum eigenvalue problems. The key point of the KEP method is to split the mass factor into effective ones, each to be associated with partial kinetic energy terms, and the full Hamiltonian of the system can be wrote as the sum of subsystem Hamiltonians. Starting from the simple one-particle problems, we gradually increase the complexity in particle number, dimension and interaction patterns. For the many-body system, we propose to use the idea of “negative mass” to deal with the repulsive interaction potential, and in order to reduce the number of basis sets with continuous-energy. In addition, to simplify the procedure of KEP method, we employ an adiabatic approximation. We will test the utility of the KEP method with the models such as Moshinsky atoms, Hookium atom and Dirackium atom which error within 5%. Furthermore, to challenge the three-body problem first, use the one-dimensional Moshinsky atoms to prove it has the opportunity to confront the quantum many-body problems. Moreover, the other part is variational kinetic energy partition method (VKEP). We study the theoretical background of the KEP method by studying its relation with the variational principles. Owing to the new variational parameters provided by the KEP method, we believe VKEP method can improve KEP method to make it more precise. We use the simplest case of double delta potential to verify its feasibility. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T06:02:04Z (GMT). No. of bitstreams: 1 ntu-108-R05543001-1.pdf: 2619818 bytes, checksum: 7ccdac79323c775778908f27b8128079 (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 口試委員會審定書 #
致謝 i 摘要 ii ABSTRACT iii 目錄 iv 圖目錄 vi 表目錄 viii 第一章 緒論 1 第二章 KEP理論介紹 4 2.1 單體之不同權重雙位能函數 4 2.2 KEP & AKEP &AVKEP Principle 8 第三章 模型系統範例 16 3.1 三維Harmonium Atoms 16 3.2 一維Dirackium atoms 29 3.3 三維Moshinsky Atoms 44 3.4 一維Moshinsky Atoms (N=2) 63 3.5 一維Moshinsky Atoms (N=3) 78 第四章 Variational KEP 94 4.1 雙負δ位能 (Double Delta Potential) 94 4.1.1 Exact Solution 94 4.1.2 The Variational Principle (Rayleigh-Ritz Approximation) 99 4.1.3 Variational KEP Principle 107 第五章 結論與展望 122 5.1 結論 122 5.2 展望 123 參考文獻 124 | |
| dc.language.iso | zh-TW | |
| dc.subject | 動能分離法 | zh_TW |
| dc.subject | 負質量 | zh_TW |
| dc.subject | 量子特徵值問題 | zh_TW |
| dc.subject | 多體薛丁格方程式 | zh_TW |
| dc.subject | 變分動能分離法 | zh_TW |
| dc.subject | negative mass | en |
| dc.subject | kinetic energy partition | en |
| dc.subject | variational kinetic energy partition | en |
| dc.subject | many-body Schrodinger equation | en |
| dc.subject | quantum eigenvalue problems | en |
| dc.title | 延伸分離動能法求解多體系統 | zh_TW |
| dc.title | Extension of Kinetic Energy Partition Method to Many-body Systems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 107-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張建成(Chien-Cheng Chang),陳國慶(Kuo-Ching Chen),鄭原忠(Yuan-Chung Cheng),林俊達(Guin-Dar Lin) | |
| dc.subject.keyword | 動能分離法,負質量,量子特徵值問題,多體薛丁格方程式,變分動能分離法, | zh_TW |
| dc.subject.keyword | kinetic energy partition,negative mass,quantum eigenvalue problems,many-body Schrodinger equation,variational kinetic energy partition, | en |
| dc.relation.page | 129 | |
| dc.identifier.doi | 10.6342/NTU201900339 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2019-01-31 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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