Abstract
We obtain the coherent states for a particle in the noncentral Hartmann potential by transforming the problem into four isotropic oscillators evolving in a parametric time. We use path integration over the holomorphic coordinates to find the quantum states for these oscillators. The decomposition of the transition amplitudes gives the coherent states and their parametric-time evolution for the particle in the Hartmann potential. We also derive the coherent states in the parabolic coordinates by considering the transition amplitudes between the coherent states and eigenstates in the configuration space.
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References
E. Schrödinger, Naturwissenschaften, 14, 664–666 (1926).
R. J. Glauber, Phys. Rev. Lett., 10, 84–86 (1963); Phys. Rev., 130, 2529–2539 (1963).
M. M. Nieto and L. M. Simmons Jr., Phys. Rev. Lett., 41, 207–210 (1978).
L. S. Brown, Amer. J. Phys., 41, 525–530 (1973).
D. Bhaumik, B. Dutta-Roy, and G. Ghosh, J. Phys. A, 19, 1355–1364 (1986).
A. ten Wolde, L. D. Noordam, A. Lagendijk, and H. B. van Linden van den Heuvell, Phys. Rev. Lett., 61, 2099–2101 (1988).
H. Goldstein, Classical Mechanics [in Russian], Nauka, Moscow (1975); English transl., Addison-Wesley, Reading, Mass. (1980).
P. Kustaanheimo and E. Stiefel, J. Reine Angew. Math., 218, 204–219 (1965).
I. H. Duru and H. Kleinert, Phys. Lett. B, 84, 185–188 (1979); Fortschr. Phys., 30, 401–435 (1982).
T. Toyoda and S. Wakayama, Phys. Rev. A, 59, 1021–1024 (1999).
N. Ünal, Found. Phys., 28, 755–762 (1998).
N. Ünal, Phys. Rev. A, 63, 2105 (2001); Turk. J. Phys., 24, 463–472 (2000).
N. Ünal, Canad. J. Phys., 80, 875–881 (2002).
N. Ünal, “Path integration and coherent states for the 5D hydrogen atom,” in: Fluctuating Paths and Fields (W. Janke, A. Pelster, and H.-J. Schmidt, eds.), World Scientific, River Edge, N. J. (2001), pp. 73–81.
T. Toyoda and S. Wakayama, Phys. Rev. A, 64, 2110 (2001).
H. Hartmann, Theor. Chim. Acta, 24, 201–206 (1972).
B. P. Mandal, Internat. J. Mod. Phys. A, 15, 1225–1234 (2000).
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatlit, Moscow (1971); English transl.: Tables of Integrals, Series, and Products, Acad. Press, New York (1980).
Gh. E. Drägänascu, C. Campigotto, and M. Kibler, Phys. Lett. A, 170, 339–343 (1992).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 439–452, June, 2008.
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Kandirmaz, N., Ünal, N. Coherent states for the Hartmann potential. Theor Math Phys 155, 884–895 (2008). https://doi.org/10.1007/s11232-008-0074-z
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DOI: https://doi.org/10.1007/s11232-008-0074-z