Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials

DOI10.1088/1751-8121/aaa553zbMath1386.81095arXiv1709.08835OpenAlexW2963858462WikidataQ57999091 ScholiaQ57999091MaRDI QIDQ5373942

Véronique Hussin, Scott E. Hoffmann, Ian Marquette, Yao-Zhong Zhang

Publication date: 6 April 2018

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.08835

zbMATH Keywords

orthogonal polynomialspolynomial algebrasquantum mechanicssupersymmetry

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Coherent states (81R30) Supersymmetry and quantum mechanics (81Q60) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Operations and polynomials in algebraic structures, primal algebras (08A40)

Related Items (6)

Controllable behavior of self-similar matter waves in exotic transient trap variations ⋮ General solution of the exceptional Hermite differential equation and its minimal surface representation ⋮ Coherent states for ladder operators of general order related to exceptional orthogonal polynomials ⋮ Coherent States in Quantum Optics: An Oriented Overview ⋮ Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations ⋮ Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties

Cites Work

• Unnamed Item
• Unnamed Item
• Coherent states, wavelets, and their generalizations
• Generalized coherent states associated with the \(C_ \lambda\)-extended oscillator.
• Even and odd nonlinear coherent states.
• Factorizations of one-dimensional classical systems
• New 'coherent' states associated with non-compact groups
• Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial
• Squeezed coherent states and the one-dimensional Morse quantum system
• Combined state-adding and state-deleting approaches to type III multi-step rationally extended potentials: Applications to ladder operators and superintegrability
• On the generalized intelligent states and certain related nonclassical states of a quantum exactly solvable nonlinear oscillator
• Coherent states for systems with discrete and continuous spectrum
• Distorted Heisenberg algebra and coherent states for isospectral oscillator Hamiltonians
• Coherent states for isospectral oscillator Hamiltonians
• Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators
• Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states
• Continuous-Representation Theory. I. Postulates of Continuous-Representation Theory
• Coherent and Incoherent States of the Radiation Field
• Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems

This page was built for publication: Non-classical behaviour of coherent states for systems constructed using exceptional orthogonal polynomials