Abstract
Gazeau-Klauder coherent states are developed for power-law potentials and their evolution in space and time is analyzed. We show that these states follow classical dynamics as long as the underlying energy spectrum is linear, otherwise they follow a classical-like evolution upto a few classical periods and disperse thereafter, despite its special construction. Auto-correlation function and probability density as a function of space and time explain the spatio-temporal behavior of these states.
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Schrödinger, E.: Naturwissenschaften 14, 664 (1926)
Glauber, R.J.: Phys. Rev. Lett. 10, 277 (1963)
Glauber, R.J.: Phys. Rev. 130, 2529 (1963)
Glauber, R.J.: Phys. Rev. 131, 2766 (1963)
Klauder, J.R., Skagerstam, B.S.: Coherent States: Applications in Physics and Mathematical Physics. Singapore, World Scientific (1985)
Perelomov, A.M.: Generalized Coherent States and Their Applications. Springer, Berlin (1986)
Glauber, R.J.: Quantum Theory of Optical Coherences. Wiley, New York (2007)
Gazeau, J.P.: Coherent States in Quantum Physics. Wiley, New York (2009)
Barut, A.O., Girardello, L.: Commun. Math. Phys. 21, 41 (1971)
Perelomov, M.: Commun. Math. Phys. 26, 222 (1972)
Klauder, J.R.: J. Math. Phys. 4, 1055 (1963)
Klauder, J.R.: J. Phys. A: Math. Gen. 29, L293 (1996)
Bellomo, P., Stroud, C.R.: J. Phys. A: Math. Gen. 31, L445 (1998)
Gazeau, J.P.G., Klauder, J.R.: J. Phys. A: Math. Gen. 32, 123 (1999)
Popov, D., Sajfert, V., Zaharie, I.: Physica A 387, 4459 (2008)
Chenaghlou, A., Faizy, O.: J. Math. Phys. 49, 022104 (2008)
Angelova, M., Hussin, V.: J. Phys. A: Math. Gen. 41, 304016 (2008)
Antoine, J.P., Gazeau, J.P.G., Monceau, P., Klauder, J.R., Penson, K.A.: J. Math. Phys. 42, 2349 (2001)
Hollingworth, J.M., Konstadopoulou, A., Chountasis, S., Vourdas, A., Backhouse, N.B.: J. Phys. A: Math. Gen. 34, 9463 (2001)
Iqbal, S., Qurat-ul-Ann, Saif, F.: Phys. Lett. A 356, 231 (2006)
Großmann, F., Rost, J.-M., Schleich, W.P.: J. Phys. A: Math. Gen. 30, L227 (1997)
Marzoli, L., Saif, F., Bialynicki-Birula, I., Friesch, M.O., Kaplan, A.E., Schleich, W.P.: Acta Phys. Slovaca 48, 323 (1998)
Sukhatme, U.P.: Am. J. Phys. 41, 1015 (1973)
Wallis, H., Dalibard, J., Cohen-Tannoudji, C.: Appl. Phys. B 54, 407 (1991)
Gea-Banacloche, J.: Am. J. Phys. 67, 776 (1999)
Klauder, J.R., Penson, K.A., Sixdeniers, J.-M.: Phys. Rev. A 64, 013817 (2001)
Nauenberg, M.: J. Phys. B: At. Mol. Opt. Phys. 23, L385 (1990)
Robinett, R.W.: Phys. Rep. 392, 1 (2004)
Buchleitner, A., Delande, D., Zakrzewskix, J.: Phys. Rep. 368, 409 (1990)
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Iqbal, S., Rivière, P. & Saif, F. Space-Time Dynamics of Gazeau-Klauder Coherent States in Power-Law Potentials. Int J Theor Phys 49, 2540–2557 (2010). https://doi.org/10.1007/s10773-010-0446-7
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DOI: https://doi.org/10.1007/s10773-010-0446-7