Quantum symmetries and solvability

量子对称性和可解性

• 批准号: 23540303
• 负责人: SASAKI Ryu
• 金额: $ 2.5万
• 依托单位: Shinshu University (2013)Kyoto University (2011-2012)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540303/
• 关键词: 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

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.

明确构造了无穷多个精确可解的一维量子力学系统，并详细讨论了它们的量子对称性和可解性。 对原始特征函数进行离散对称变换，得到（伪）虚态波函数。对虚态进行多次达布变换，得到多指标正交多项式。许多朗斯基和卡索拉恒等式都是通过伪虚态的变形导出的。原始系统是（径向）谐振子、Poschl-Teller、莫尔斯、埃卡特、普通量子力学中的库仑势以及威尔逊、阿斯基-威尔逊和（q- ）来自离散量子力学的 Racah 多项式系统。具有较高视奇点度的多索引拉盖尔和雅可比多项式也与相应的势一起构造。

项目成果

Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials

精确可解的量子力学和多索引正交多项式的无限族

• DOI: 10.1016/j.physletb.2011.06.075
• 发表时间: 2011
• 期刊: Phys. Lett
• 作者: S.Matsuzaki;K.Yamawaki;江尻信司;片岡啓介;S. Odake and R. Sasaki
• 通讯作者: S. Odake and R. Sasaki

Exactly Solvable Birth and Death Processes, Special Functions Day

精确可解的出生和死亡过程，特殊函数日

• 发表时间: 2013
• 作者: 筒井亮;中村卓史;米徳大輔;高橋慶太郎;山脇幸一;R. Sasaki
• 通讯作者: R. Sasaki

Scattering amplitudes for multi-indexed extensions of solvable potentials

• DOI: 10.1016/j.aop.2014.01.015
• 发表时间: 2013-09
• 期刊: Annals of Physics
• 影响因子: 3
• 作者: C.-L. Ho;J.-C. Lee;R. Sasaki

Exactly solvable potentials with finitely many discrete eigenvalues of arbitrary choice

• DOI: 10.1063/1.4880200
• 发表时间: 2014-02
• 期刊: Journal of Mathematical Physics
• 影响因子: 1.3
• 作者: R. Sasaki

Multi-indexed ($q$-)Racah polynomials

多索引 ($q$-)Racah 多项式

• DOI: 10.1088/1751-8113/45/38/385201
• 发表时间: 2012
• 期刊: Journal of Physics A
• 作者: 笠松健一;一瀬郁夫;松居哲生;S. Odake and R. Sasaki
• 通讯作者: S. Odake and R. Sasaki