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References 188 Carruthers, P and Nieto, MM (1968) Phase and Angle Variables in Quantum Mechanics, Rev Mod Phys, 40, 411 189 Louisell, WH (1963) Amplitude and phase uncertainty relations, Phys Lett, 7, 60 190 Susskind, L and Glogower, J (1964) Quantum mechanical phase and time operator, Physics, 1, 49 191 Popov, VN and Yarunin, VS (1973) Quantum and quasi-classical states of the photon phase operator, Vestnik Leningrad University, 22, 7 192 Popov, VN and Yarunin, VS (1992) Quantum and Quasi-classical States of the Photon Phase Operator, J Mod Opt, 39, 1525 193 Barnett, SM and Pegg, DT (1989) Phase in quantum optics, J Mod Opt, 36, 7 194 Busch, P, Grabowski, M and Lahti, PJ (1995) Who is afraid of POV measures Uni ed approach to quantum phase observables, Ann Phys (NY), 237, 1 195 Busch, P, Lahti, P, Pellonpa, J-P and Ylinen, K (2001) Are number and phase complementary observables J Phys A: Math Gen, 34, 5923 196 Dubin, DA, Hennings, MA and Smith, TB (1994) Quantization in polar coordinates and the phase operator, Publ Res Inst Math Sci, 30, 479 197 Busch, P, Hennings, MA and Smith, TB (2000) Mathematical Aspects of Weyl Quantization and Phase, World Scienti c, Singapore 198 Gazeau, J-P, Piechocki, W (2004) Coherent state quantization of a particle in de Sitter space, J Phys A: Math Gen, 37, 6977 199 Garcia de Leon, P, Gazeau, J-P and Qu va, J (2008) The in nite well revisited: coherent states and quantization, Phys Lett A, 372, 3597 200 Garcia de Leon, P, Gazeau, J-P, Gitman, D, and Qu va, J (2009) In nite quantum well: on the quantization problem, Quantum Wells: Theory, Fabrication and Applications Nova Science Publishers, Inc 201 Ashtekar, A, Fairhurst, S and Willis, JL (2003) Quantum gravity, shadow states, and quantum mechanics, Class Quantum Grav, 20, 1031 202 L vy-Leblond, JM (2003) Who is afraid of Nonhermitian Operators A quantum description of angle and phase, Ann Phys, 101, 319 203 Rabeie, A, Huguet, E and Renaud, J (2007) Wick ordering for coherent state quantization in 1 + 1 de Sitter space, Phys Lett A, 370, 123 204 Znojil, M (2001) PT -symmetric square well, Phys Lett A, 285, 7 205 Ali, ST, Engli , M and Gazeau, J-P (2004) Vector coherent states from Plancherel s theorem, Clifford algebras and matrix domains, J Phys A: Math Gen, 37, 6067 206 Reed, M and Simon, B (1980) Methods of Modern Mathematical Physics, Functional Analysis vol I, Academic Press, New York 207 Lagarias, J (2000) Mathematical Quasicrystals and the Problem of Diffraction, in Directions in Mathematical Quasicrystals (eds Baake, M and Moody, RV), CRM monograph Series, Am Math Soc, Providence, RI 208 Bouzouina, A, and De Bi vre, S (1996) Equipartition of the eigenfunctions of quantized ergodic maps on the torus, Commun Math Phys, 178, 83 209 Abramowitz, M and Stegun, IA (1972) Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series 55 210 Calderon, AP and Vaillancourt, R (1972) A class of bounded pseudodifferential operators, Proc Natl Acad Sci USA, 69, 1185 211 Bouzouina, A and De Bi vre, S (1998) Equidistribution des valeurs propres et ergodicit semi-classique de symplectomorphismes du tore quanti s, C R Acad Sci, S rie I, 326, 1021 212 Gazeau, J-P, Huguet, E, Lachi ze Rey, M and Renaud, J (2007) Fuzzy spheres from inequivalent coherent states quantizations, J Phys A: Math Theor, 40, 10225 213 Grosse, H and Pre najder, P (1993) The construction of non-commutative manifolds using coherent states, Lett Math Phys, 28, 239 214 Kowalski, K and Rembielinski, J (2000) Quantum mechanics on a sphere and coherent states, J Phys A: Math Gen, 33, 6035.



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References 215 Kowalski, K and Rembielinski, J (2001) The Bargmann representation for the quantum mechanics on a sphere, J Math Phys, 42, 4138 216 Hall, B and Mitchell, JJ (2002) Coherent states on spheres, J Math Phys, 43, 1211 217 Freidel, L and Krasnov, K (2002) The fuzzy sphere -product and spin networks, J Math Phys, 43, 1737 218 Gazeau, J-P, Mourad, J and Qu va, J (2009) Fuzzy de Sitter space-times via coherent states quantization, in Proceedings of the XXVIth Colloquium on Group Theoretical Methods in Physics, New York, USA, 2006 (eds Birman, J and Catto, S) to appear 219 Gazeau, J-P (2007) An Introduction to Quantum Field Theory in de Sitter space-time, in Cosmology and Gravitation: XIIth Brazilian School of Cosmology and Gravitation (eds Novello, M and Perez-Bergliaffa, SE), AIP Conference Proceedings 910, 218 220 Sinai, YG (1992) Probability Theory An introductory Course, Springer Textbook, Springer-Verlag, Berlin 221 Johnson, NL and Kotz, S (1969) Discrete Distributions, John Wiley & Sons, Inc, New York 222 Ross, SM (1985) Introduction to Probability Models Academic Press, New York 223 Douglas, JB (1980) Analysis with Standard Contagious Distributions, International Co-operative Publishing House, Fairland, Maryland 224 Vilenkin, NY (1968) Special Functions and the Theory of Group Representations, Am Math Soc, Providence, RI 225 Barut, AO and Raczka, R (1977) Theory of Group Representations and Applications, PWN, Warszawa 226 Kirillov, AA (1976) Elements of the Theory of Representations, Springer-Verlag, Berlin 227 Arfken, G (1985) Spherical Harmonics and Integrals of the Products of Three Spherical Harmonics 126 and 129 in Mathematical Methods for Physicists, p 680 and p 698, 3rd ed, Academic Press, Orlando, FL 228 Weisstein, EW Spherical Harmonic, MathWorld A Wolfram Web Resource http://mathworldwolframcom/ SphericalHarmonichtml

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