论文标题
新的有限型多指数正交多项式从国家添加Darboux转换获得
New Finite Type Multi-Indexed Orthogonal Polynomials Obtained From State-Adding Darboux Transformations
论文作者
论文摘要
有限型离散量子力学的汉密尔顿人具有真实偏移的量子机制是订单$ n+1 $的真实对称矩阵。我们讨论了较高度（$> n $）多项式解决方案的Darboux转换。他们是国家额外的，在$ m $ steps之后，由此产生的哈密顿人是$ n+m+1 $的订单。 Based on twelve orthogonal polynomials (($q$-)Racah, (dual, $q$-)Hahn, Krawtchouk and five types of $q$-Krawtchouk), new finite type multi-indexed orthogonal polynomials are obtained, which satisfy second order difference equations, and all the eigenvectors of the deformed Hamiltonian are described by them.我们还提出了Krein-Adler型多族裔正交多项式及其差异方程的明确形式，这些方程是从较低度（$ \ leq n $）多项式溶液作为种子溶液的状态填充的Darboux变换获得的。
The Hamiltonians of finite type discrete quantum mechanics with real shifts are real symmetric matrices of order $N+1$. We discuss the Darboux transformations with higher degree ($>N$) polynomial solutions as seed solutions. They are state-adding and the resulting Hamiltonians after $M$-steps are of order $N+M+1$. Based on twelve orthogonal polynomials (($q$-)Racah, (dual, $q$-)Hahn, Krawtchouk and five types of $q$-Krawtchouk), new finite type multi-indexed orthogonal polynomials are obtained, which satisfy second order difference equations, and all the eigenvectors of the deformed Hamiltonian are described by them. We also present explicit forms of the Krein-Adler type multi-indexed orthogonal polynomials and their difference equations, which are obtained from the state-deleting Darboux transformations with lower degree ($\leq N$) polynomial solutions as seed solutions.
