Spectral analysis of q-oscillator with general bilinear interaction

Journal of Physics A: Mathematical and General

Volumn 31, Issue 45, 1998, Pages 9081-9094

  Loutsenko, I ^a   Spiridonov, V ^b   Vinet, L ^a   Zhedanov, A ^c  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^c DONETSK PHYSICOTECHNICAL INSTITUTE   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032514825     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/45/008     Document Type: Article

References (24)

1. q J. Phys. A: Math. Gen. 22 4581-8
2. Fivel D I 1991 Quasi-coherent states and the spectral resolution of the q-Bose field operator J. Phys. A: Math. Gen. 24 3573-86
3. Floreanini R and Vinet L 1991 q-orthogonal polynomials and the oscillator quantum group Lett. Math. Phys. 22 45-54
4. Zhedanov A S 1991 Nonlinear shift of q-Bose operators and q-coherent states J. Phys. A: Math. Gen. 24 L1129-32
5. Spiridonov V 1992 Exactly solvable potentials and quantum algebras Phys. Rev. Lett. 69 398-401
6. Skorik S and Spiridonov V 1993 Self-similar potentials and the q-oscillator algebra at roots of unity Lett. Math. Phys. 28 59-74
7. Spiridonov V, Vinet L and Zhedanov A 1993 Difference Schrödinger operators with linear and exponential discrete spectra Lett. Math. Phys. 29 63-73
8. Floreanini R and Vinet L 1993 Quantum algebras and q-special functions Ann. Phys., NY 221 53-70
9. Granovskii Ya I and Zhedanov A S 1993 Production of q-bosons by a classical current: an exactly solvable model Mod. Phys. Lett. A 9 1029-35
10. q(2) J. Group Theory Phys. 1 161-71
11. Askey R and Suslov S 1993 The q-harmonic oscillator and the Al-Salam and Carlitz polynomials Lett. Math. Phys. 29 123-32
12. Spiridonov V 1995 Coherent states of the q-Weyl algebra Lett. Math. Phys. 35 179-85
13. Spiridonov V 1995 Universal superpositions of coherent states and self-similar potentials Phys. Rev. A 52 1909-35 Spiridonov V 1995 Phys. Rev. A 53 2903 (erratum)
14. Spiridonov V 1995 Universal superpositions of coherent states and self-similar potentials Phys. Rev. A 52 1909-35 Spiridonov V 1995 Phys. Rev. A 53 2903 (erratum)
15. Lutzenko I, Spiridonov V and Zhedanov A 1995 On the spectrum of a q-oscillator with a linear interaction Phys. Lett. A 204 236-42
16. Bozejko M, Kümmerer B and Speicher R 1997 q-Gaussian process: non-commutative and classical aspects Commun. Math. Phys. 185 129-54
17. Frisch U and Bourret R 1970 Parastochastics J. Math. Phys. 11 364-90
18. Arik M and Coon D 1976 Hilbert spaces of analytic functions and generalized coherent states J. Math. Phys. 17 524-7
19. Infeld L and Hull T E 1951 The factorization method Rev. Mod. Phys. 23 21-68
20. Gasper G and Rahman M 1990 Basic Hypergeometric Series (Cambridge: Cambridge University Press)
21. Koekoek R and Swarttouw R F 1994 The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Report 94-05, Delft University
22. Derfel G A and Molchanov S A 1990 Spectral methods in the theory of differential-functional equations Mat. Zametki 47 42-51
23. Kato T and McLeod J B 1971 The functional-differential equation y′(x) = ay(λx) + by(x) Bull. Am. Math. Soc. 77 891-937
24. Iseries A 1993 On the generalized pantograph functional-differential equation Eur. J. Appl. Math. 4 1-38