# Quantum models with spectrum generated by the flows of polynomial zeros

@article{Moroz2014QuantumMW,
title={Quantum models with spectrum generated by the flows of polynomial zeros},
author={Alexander Moroz},
journal={Journal of Physics A},
year={2014},
volume={47},
pages={495204}
}
• A. Moroz
• Published 15 March 2014
• Mathematics
• Journal of Physics A
A class of purely bosonic models is characterized having the following properties in a Hilbert space of analytic functions: (i) wave function is the generating function for orthogonal polynomials of a discrete energy variable , (ii) any Hamiltonian has nondegenerate purely point spectrum that corresponds to infinite discrete support of measure in the orthogonality relation of the polynomials , (iii) the support is determined exclusively by the points of discontinuity of , (iv) the spectrum of…
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## References

SHOWING 1-10 OF 82 REFERENCES
Quasi-exactly-solvable problems andsl(2) algebra
Recently discovered quasi-exactly-solvable problems of quantum mechanics are shown to be related to the existence of the finite-dimensional representations of the groupSL(2,Q), whereQ=R, C. It is
A system of three quantum particles with point-like interactions
Consider a?quantum three-particle system consisting of two fermions of unit mass and another particle of mass interacting in a point-like manner with the fermions. Such systems are studied here using
On the spectrum of a class of quantum models
The spectrum of any quantum model whose eigenvalue equation reduces to a three-term recurrence, such as a displaced harmonic oscillator, the Jaynes-Cummings model, the Rabi model, and a generalized
Orthogonal Polynomials from Hermitian Matrices
• Mathematics
• 2008
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of Hermitian matrices of finite or infinite dimensions. It can be considered as a matrix
Quasi‐exactly solvable systems and orthogonal polynomials
• Physics
• 1995
This paper shows that there is a correspondence between quasi‐exactly solvable models in quantum mechanics and sets of orthogonal polynomials {Pn}. The quantum‐mechanical wave function is the
Hill?s determinant approach to single-mode spin-boson model
• Physics
• 2013
An efficient and stable numerical scheme based on Hill’s determinant is proposed for computing the whole spectrum of the single-mode spin-boson model. Its shown that for the low-lying levels a simple