Quantum symmetries and solvability
| Project/Area Number |
23540303
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Shinshu University (2013)
Kyoto University (2011-2012) |
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Principal Investigator |
SASAKI Ryu 信州大学, 理学部, 特任教授 (20154007)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKASAKI Kanehisa 京都大学, 人間環境学研究科, 教授 (40171433)
ODAKE Satoru 信州大学, 理学部, 教授 (40252051)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 可解量子力学 / 離散量子力学 / 量子対称性 / 有理型変形 / ダルブー変換 / カソラティアン / q-直交多項式 / 量子dilog関数 / 量子diLog関数 / 国際研究者交流 / 多添え字直交多項式 / 多添え字ウィルソン多項式 / 多添え字アスキー・ウィルソン多項式 / フックス型微分方程式 / 有理関数解 / 高次の極 / 見かけの特異性の合流 / 国際情報交流 / 例外直交多項式 / 多添え字ラゲール多項式 / 多添え字ジャコビ多項式 / 多添え字(q)-ラカー多項式 |
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| Research Abstract |
Infinitely many exactly solvable 1-d quantum mechanical systems are constructed explicitly and their quantum symmetries and solvability are discussed in detail. (Pseudo) virtual state wavefunctions are obtained by applying discrete symmetry transformations to the original eigenfunctions.Multi-indexed orthogonal polynomials are obtained by using multiple Darboux transformations in terms of virtual states. Many Wronskian and Casoratian identities are derived through deformations in terms of pseudo virtual states.The original systems are (radial) harmonic oscillator, Poschl-Teller, Morse, Eckart, Coulomb potentials from ordinary quantum mechanics and Wilson, Askey-Wilson and (q-)Racah polynomial systems from discrete quantum mechanics. Multi-indexed Laguerre and Jacobi polynomials having higher degree of apparent singularities are also constructed together with the corresponding potentials.
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Report
(4 results)
Research Products
(39 results)
