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6 papers · 2 filters
Reflectionless Potentials for Difference Schrödinger Equations
Satoru Odake, Ryu Sasaki
As a part of the program `discrete quantum mechanics,' we present general reflectionless potentials for difference Schrödinger equations with pure imaginary shifts. By combining co…
Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
Satoru Odake
In a previous paper we presented term recurrence relations with variable dependent coefficients for -indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-…
Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
Satoru Odake, Ryu Sasaki
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonalit…
Composition of Two Potentials
Khosrow Chadan, Reido Kobayashi, Ryu Sasaki
Given two potentials V0 and V1 together with a certain nodeless solution ϕ0 of V0, we form a composition of these two potentials. If V1 is exactly solvable, the composition is exac…
Exactly solvable potentials with finitely many discrete eigenvalues of arbitrary choice
Ryu Sasaki
We address the problem of possible deformations of exactly solvable potentials having finitely many discrete eigenvalues of arbitrary choice. As Kay and Moses showed in 1956, refle…
Classification of "Real" Bloch-bundles: Topological quantum systems of type AI
Giuseppe De Nittis, Kiyonori Gomi
We provide a classification of type AI topological quantum systems in dimension d=1,2,3,4 which is based on the equivariant homotopy properties of "Real" vector bundles. This allow…