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6 papers · 2 filters
Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials
Satoru Odake, Ryu Sasaki
We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X_{\ell}) Laguerre polynomials. They are to supplement the recently derived tw…
Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
Satoru Odake, Ryu Sasaki
We provide analytic proofs for the shape invariance of the recently discovered (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417) two families of infinitely many exactly solvable…
Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
Satoru Odake, Ryu Sasaki
Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape inv…
Infinitely many shape invariant potentials and new orthogonal polynomials
Satoru Odake, Ryu Sasaki
Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the…
Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
Satoru Odake, Ryu Sasaki
We present a simple recipe to construct exactly and quasi-exactly solvable Hamiltonians in one-dimensional `discrete' quantum mechanics, in which the Schrödinger equation is a diff…
Crum's Theorem for `Discrete' Quantum Mechanics
Satoru Odake, Ryu Sasaki
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which ar…