Representations of coherent states in non-orthogonal bases

Journal of Physics A: Mathematical and General

Volumn 37, Issue 15, 2004, Pages 4407-4422

  Ali, S Twareque ^a   Roknizadeh, R ^b   Tavassoly, M K ^b  

^a Dept of Electrical and Computer Engineering   (Canada)

^b UNIVERSITY OF ISFAHAN   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2142712997     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/15/009     Document Type: Article

References (23)

1. Agarwal G K and Tara K 1991 Non-classical properties of states generated by the excitations on a coherent state Phys. Rev. A 43 492-7
2. Ali S T, Antoine J-P and Gazeau J-P 2000 Coherent States, Wavelets and Their Generalizations (New York: Springer)
3. Antoine J-P, Inoue A and Trapani C 2002 Partial *-algebras and their operator realizations Mathematics and Its Applications vol 553 (Dordrecht: Kluwer)
4. Appl T and Schiller D H 2003 Generalized hypergeometric coherent states Preprint quant-ph0308013
5. Barut A O and Girardello L 1971 New 'coherent' states associated with non-compact groups Commun. Math. Phys. 21 41-55
6. Beckers J, Cariñena J F, Debergh N and Marmo G 2001 Non-Hermitian oscillator-like Hamiltonians and λ-coherent states revisited Mod. Phys. Lett. A 16 91-8
7. Beckers J, Debergh N and Szafraniec F H 1998a A proposal of new sets of squeezed states Phys. Lett. A 243 256-60
8. Beckers J, Debergh N and Szafraniec F H 1998b Phys. Lett. A 246 561
9. Borzov V V, Damaskinsky E V and Yegorov S B 1995 Some remarks on the representations of the generalized deformed oscillator algebra Preprint q-alg/9509022
10. Borzov V V, Damaskinsky E V and Yegorov S B 1997 Zap. Nauchn. Semin. LOMI 245 80-106 (in Russian)
11. Filho R L, de Matos and Vogel W 1996 Nonlinear coherent states Phys. Rev. A 54 4560-63
12. Fu H, Feng Y and Solomon A I 2000 States interpolating between number'and coherent states and their interaction with atomic systems J. Phys. A: Math. Gen. 33 2231-49
13. Gazeau J-P and Klauder J R 1999 Coherent states for systems with discrete and continuous spectrum J. Math. Phys. A 32 123-32
14. Gelfand I M and Vilenkin N Ya 1964 Generalized Functions vol 4 (New York: Academic)
15. Gilmore R 1974 Lie Groups, Lie Algebras, and Some of Their Applications (New York: Wiley)
16. Klauder J R and Skagerstam B S 1985 Coherent States, Applications in Physics and Mathematical Physics (Singapore: World Scientific)
17. Man'ko V I, Marmo G, Sudarshan E C G and Zaccaria F 1997 f-oscillators and non-linear coherent states Phys. Scr. 55 528-41
18. Odzijewicz A 1998 Quantum algebras and q-special functions related to coherent states maps of the disc Commun. Math. Phys. 192 183-215
19. Perelomov A M 1986 Generalized Coherent States and Their Applications (Berlin: Springer)
20. Roy A K and Mehta C L 1995 Boson inverse operators and associated coherent states Quantum Semiclass. Opt 7 877-88
21. Roy B and Roy P 2000 New nonlinear coherent states and some of their nonclassical properties J. Opt. B: Quantum Semiclass. Opt. 2 65-8
22. Simon R, Sudarshan ECO and Mukunda N 1988 Gaussian pure states in quantum mechanics and the symplectic group Phys. Rev. A 37 3028-38
23. Sugiura M 1990 Unitary Representations and Harmonic Analysis: An Introduction (Tokyo: North-Holland/Kodansha Ltd)