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Reflectionless potentials for difference Schrodinger equations
http://hdl.handle.net/10091/18500
http://hdl.handle.net/10091/18500dffcf14a-5145-4ed2-96f1-d938a5c7ca99
| 名前 / ファイル | ライセンス | アクション |
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Reflectionless_Potentials_for_Difference.pdf (276.6 kB)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||||||
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| 公開日 | 2015-07-07 | |||||||||
| タイトル | ||||||||||
| タイトル | Reflectionless potentials for difference Schrodinger equations | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| DOI | ||||||||||
| 関連識別子 | https://doi.org/10.1088/1751-8113/48/11/115204 | |||||||||
| 関連名称 | 10.1088/1751-8113/48/11/115204 | |||||||||
| キーワード | ||||||||||
| 主題 | scattering problems in discrete QM, solvable scattering problems, Heine' s hypergometric functions with, q, =1, connection formula for 2.1, with, q, =1, q, ultraspherical polynomials with, q, =1, quantum dilogarithm, discrete analogue of 1 cosh2x potential | |||||||||
| 資源タイプ | ||||||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||||||
| タイプ | journal article | |||||||||
| 著者 |
Odake, Satoru
× Odake, Satoru
× Sasaki, Ryu
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| 信州大学研究者総覧へのリンク | ||||||||||
| 氏名 | Odake, Satoru | |||||||||
| URL | http://soar-rd.shinshu-u.ac.jp/profile/ja.uhLeuUkV.html | |||||||||
| 出版者 | ||||||||||
| 出版者 | IOP PUBLISHING LTD | |||||||||
| 引用 | ||||||||||
| 内容記述 | JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 48(11):115204 (2015) | |||||||||
| 書誌情報 |
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 巻 48, 号 11, p. 115204, 発行日 2015-03-20 |
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| 抄録 | ||||||||||
| 内容記述 | As a part of the program 'discrete quantum mechanics', we present general reflectionless potentials for difference Schr dinger equations with pure imaginary shifts. By combining contiguous integer wave number reflectionless potentials, we construct the discrete analogues of the h(h＋1)/cosh²x potential with the integer h, which belong to the recently constructed families of solvable dynamics having the q-ultraspherical polynomials with |q| = 1 as the main part of the eigenfunctions. For the general h ∈R>o<br/> scattering theory for these potentials, we need the connection formulas for the basic hypergeometric function. a b c 2 1, q; z...... with |q| = 1, which is not known. The connection formulas are expected to contain the quantum dilogarithm functions as the |q| = 1 counterparts of the q-gamma functions. We propose a conjecture of the connection formula of the 2.1 function with |q| = 1. Based on the conjecture, we derive the transmission and reflection amplitudes, which have all the desirable properties. They provide a strong support to the conjectured connection formula. | |||||||||
| 資源タイプ（コンテンツの種類） | ||||||||||
| ISSN | ||||||||||
| 収録物識別子タイプ | ISSN | |||||||||
| 収録物識別子 | 1751-8113 | |||||||||
| 書誌レコードID | ||||||||||
| 収録物識別子タイプ | NCID | |||||||||
| 収録物識別子 | AA12185372 | |||||||||
| 権利 | ||||||||||
| 権利情報 | This is an author-created, un-copyedited version of an article accepted for publication in JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at 10.1088/1751-8113/48/11/115204© 2015 IOP Publishing Ltd | |||||||||
| 出版タイプ | ||||||||||
| 出版タイプ | AM | |||||||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||
| WoS | ||||||||||
| URL | http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=ShinshuUniv&SrcApp=ShinshuUniv&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000350631300006 | |||||||||
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Cite as
Odake, Satoru, Sasaki, Ryu, 2015, Reflectionless potentials for difference Schrodinger equations: IOP PUBLISHING LTD, 115204– p.
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