Some physical appearances of vector coherent states and coherent states related to degenerate Hamiltonians

Journal of Mathematical Physics

Volumn 46, Issue 5, 2005, Pages

  Ali, S Twareque ^a   Bagarello, F ^b  

^a Gina Cody School of Engineering and Computer Science   (Canada)

^b UNIVERSITY OF PALERMO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18844383716     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1901343     Document Type: Article

References (20)

1. Agarwal, G. S. and Tara, K., " Nonclassical properties of states generated by the exitations on a coherent state., " Phys. Rev. A 43, 492-497 (1991).
2. Ali, S. T., Antoine, J.-P., and Gazeau, J.-P., Coherent States, Wavelets and their Generalizations (Springer-Verlag, New York, 2000).
3. Ali, S. T. and Emch, G. G., " Geometric quantization: Modular reduction theory and coherent states., " J. Math. Phys. 27, 2936-2943 (1986).
4. Ali, S. T., Engliš, M., and Gazeau, J.-P., " Vector coherent states from Plancherel's theorem, Clifford algebras and matrix domains., " J. Phys. A 37, 6067-6089 (2004).
5. Antoine, J. P. and Bagarello, F., " Localization properties and wavelet-like orthonormal bases for the lowest Landau level., " in Advances in Gabor Analysis, edited by, H. G. Feichtinger, and, T. Strohmer, (Birkhäuser, Boston, 2003).
6. Aronszajn, A., " Theory of reproducing kernels., " Trans. Am. Math. Soc. 66, 337-404 (1950).
7. Bagarello, F., Morchio, G., and Strocchi, F., " Quantum corrections to the Wigner crystal. An Hartree-Fock expansion., " Phys. Rev. B 48, 5306-5314 (1993).
8. Fox, R. F. and Choi, M. H., " Generalized coherent states for systems with degenerate energy spectra., " Phys. Rev. A 64, 042104-042109 (2001).
9. Gazeau, J. P., Hsiao, P. Y., and Jellal, A., " Exact trace formulas for two-dimensional electron magnetism., " Phys. Rev. B 65, 094427 (2002).
10. Gazeau, J. P. and Klauder, J. R., " Coherent states for systems with discrete and continuous spectrum., " J. Phys. A 32, 123-132 (1999).
11. Gazeau, J. P. and Monceau, P., " Generalized coherent states for arbitrary quantum systems., " in Conf́rence Mosh́ Flato 1999-Quantization, Deformation and Symmetries, edited by, G. Dito, and, D. Sternheimer, (Kluwer Academic, Dordrecht, 2000), Vol. II, pp. 131-144.
12. Gazeau, J. P. and Novaes, M., " Multidimensional generalized coherent states., " J. Phys. A 36, 199-212 (2003).
13. Girvin, S. M., The Quantum Hall Effect: Novel Excitations and Broken Symmetries (Springer-Verlag, New York, 1999).
14. Haag, R., Hugenholtz, N., and Winnink, M., " On the equilibrium states in quantum statistical mechanics., " Commun. Math. Phys. 5, 215-236 (1967).
15. Klauder, J. R., " Coherent states for the hydrogen atom., " J. Phys. A 29, L293-L298 (1996).
16. Meschkowsky, H., Hilbertsche Räume mit Kernfunktionen (Springer-Verlag, Berlin, 1962).
17. Simon, D. T. and Geller, M. R., " Electron-phonon dynamics in an ensemble of nearly isolated nanoparticles., " Phys. Rev. B 64, 224504 (2001).
18. Takesaki, M., Tomita's Theory of Modular Hilbert Algebras and its Applications, Lect. Notes Math. Vol. 128 (Springer-Verlag, Berlin, 1970).
19. Takesaki, M., Theory of Operator Algebras. I (Springer-Verlag, New York, 1979).
20. Thirulogasanthar, K. and Ali, S. T., " A class of vector coherent states defined over matrix domains., " J. Math. Phys. 44, 5070-5083 (2003).