A realization for the \(q\)-harmonic oscillator

DOI10.1007/BF01016585zbMath1189.81100MaRDI QIDQ982095

Sergei K. Suslov, Natig M. Atakishiyev

Publication date: 5 July 2010

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

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (13)

Relative Fisher information of discrete classical orthogonal polynomials ⋮ Difference ladder operators for a harmonic Schrödinger oscillator using unitary linear lattices ⋮ Asymptotics of basic Bessel functions and \(q\)-Laguerre polynomials ⋮ Recurrence relations for discrete hypergeometric functions ⋮ A simple difference realization of the Heisenberg q-algebra ⋮ \textit{À la carte} recurrence relations for continuous and discrete hypergeometric functions ⋮ On the spectrum of a \(q\)-oscillator with a linear interaction ⋮ Compactness property of Lie polynomials in the creation and annihilation operators of the \(q\)-oscillator ⋮ Factorization method applied to the second order \(q\)-difference operators ⋮ Second order \(q\)-difference equations solvable by factorization method ⋮ \(q\)-classical orthogonal polynomials: A general difference calculus approach ⋮ On theq-polynomials in the exponential latticex(s)=c₁q^s+c₃ ⋮ Difference Schrödinger operators with linear and exponential discrete spectra

Cites Work

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• Classical orthogonal polynomials of a discrete variable continuous orthogonality relation
• The covariant linear oscillator and generalized realization of the dynamical SU(1,1) symmetry algebra
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• The quantum group SU_q(2) and a q-analogue of the boson operators
• On the q oscillator and the quantum algebra su_q(1,1)
• Hilbert spaces of analytic functions and generalized coherent states

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