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8 papers · 2 filters
Equivalences of the Multi-Indexed Orthogonal Polynomials
Satoru Odake
Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual state…
Casoratian Identities for the Wilson and Askey-Wilson Polynomials
Satoru Odake, Ryu Sasaki
Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomia…
Non-polynomial extensions of solvable potentials a la Abraham-Moses
Satoru Odake, Ryu Sasaki
Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics. Here w…
Spectrum of the Laplacian on a covering graph with pendant edges I: The one-dimensional lattice and beyond
Aktito Suzuki
In this paper, we examine covering graphs that are obtained from the -dimensional integer lattice by adding pendant edges. In the case of , we show that the Laplacian on th…
Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing
Fumio Hiroshima, Itaru Sasaki
The lowest eigenvalue of non-commutative harmonic oscillators is studied. It is shown that can be decomposed into four self-adjoint operators, and all the eigenvalues of ea…
Hidden Nambu mechanics - A variant formulation of Hamiltonian systems -
Atsushi Horikoshi, Yoshiharu Kawamura
We propose a variant formulation of Hamiltonian systems by the use of variables including redundant degrees of freedom. We show that Hamiltonian systems can be described by extende…
Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
Satoru Odake
Ordinary orthogonal polynomials are uniquely characterized by the three term recurrence relations up to an overall multiplicative constant. We show that the newly discovered M-inde…
Extensions of solvable potentials with finitely many discrete eigenstates
Satoru Odake, Ryu Sasaki
We address the problem of rational extensions of six examples of shape-invariant potentials having finitely many discrete eigenstates. The overshoot eigenfunctions are proposed as…