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5 papers · 2 filters
Absence of ground state for the Nelson model on static space-times
Christian Gérard, Fumio Hiroshima, Annalisa Panati +1
We consider the Nelson model on some static space-times and investigate the problem of absence of a ground state. Nelson models with variable coefficients arise when one replaces i…
A new family of shape invariantly deformed Darboux-Pöschl-Teller potentials with continuous \ell
Satoru Odake, Ryu Sasaki
We present a new family of shape invariant potentials which could be called a ``continuous \ell version" of the potentials corresponding to the exceptional (X_{\ell}) J1 Jacobi pol…
Infrared problem for the Nelson model on static space-times
Christian Gérard, Fumio Hiroshima, Annalisa Panati +1
We consider the Nelson model with variable coefficients and investigate the problem of existence of a ground state and the removal of the ultraviolet cutoff. Nelson models with var…
Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
Satoru Odake, Ryu Sasaki
An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009. Darboux-Crum tr…
Modification of Crum's Theorem for `Discrete' Quantum Mechanics
Leonor Garcia-Gutierrez, Satoru Odake, Ryu Sasaki
Crum's theorem in one-dimensional quantum mechanics asserts the existence of an associated Hamiltonian system for any given Hamiltonian with the complete set of eigenvalues and eig…