Exactly Solvable Quantum Mechanics and New Orthogonal Polynomials

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400395
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Shinshu University
• Principal Investigator: ODAKE Satoru 信州大学, 学術研究院理学系, 教授 (40252051)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 解ける量子力学模型 / 離散量子力学 / 例外・多添字直交多項式 / アスキースキームの直交多項式 / 再帰関係式 / 無反射ポテンシャル / 量子ダイログ関数 / 行列式表示

Outline of Final Research Achievements

A new type of orthogonal polynomial, which forms a complete set in spite of missing degrees, has been energetically studied since the discovery in 2008, and the reporters have constructed this new type of orthogonal polynomial, multi-indexed orthogonal polynomial, for fundamental polynomials. For this new type of orthogonal polynomial, the three term recurrence relation, which is the characterization of ordinary orthogonal polynomial, does not hold, and certain recurrence relations with more terms were expected. We obtain them explicitly and the creation/annihilation operators are constructed by using them. This research and research to increase the list of multi-indexed orthogonal polynomials are done by using quantum mechanical formulation and many new exactly solvable quantum mechanical models are obtained.

Free Research Field

物理学（数理物理学，素粒子理論）