2013 Fiscal Year Final Research Report
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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| 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 |
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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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