Abstract
The properties of the system of eigenvectors of the annihilation operator are investigated for the case of non-classical commutation relations between the operators of creation and annihilation. The existence of a measure on the set of eigenvalues of the annihilation operator is proved, with respect to which coherent states form a generalized crowded system. Formulas of covariant symbols of vectors and operators in the representation of generalized coherent states are obtained. It is shown that, similarly to the classical boson case, generalized coherent states are states with minimal uncertainty.
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REFERENCES
R. J. Glauber, Physics of Quantum Electronics, Ed. by P. L. Kelley, B. Lax, and P. E. Tannenvald (McGraw-Hill, New York, 1966).
R. J. Glauber, Quantum Optics, Ed. by R. J. Glauber (Academic, New York, 1969).
F. A. Berezin, Second Quantization Method (Nauka, Moscow, 1986) [in Russian].
J. Perina, Quantum Statistics of Linear and Nonlinear Optical Phenomena (Springer, Berlin, 1987).
Yu. N. Orlov and V. V. Vedenyapin, ‘‘Special polynomials in problems of quantum optics,’’ Mod. Phys. Lett. B 9, 291–298 (1995).
V. V. Vedenyapin, O. V. Mingalev, and I. V. Mingalev, ‘‘Representations of general commutation relations,’’ Theor. Math. Phys. 113, 369–383 (1997).
P. Aniello, V. Man’ko, G. Marmo, S. Solimeno, and F. Zaccaria, ‘‘On the coherent states, displacement operators and quasidistributions associated with deformed quantum oscillators,’’ J. Opt. B: Quantum Semiclass. Opt. 2, 718–725 (2000).
L. A. Borisov, Yu. N. Orlov, and V. Zh. Sakbaev, ‘‘Chernoff equivalence for shift operators, generating coherent states in quantum optics,’’ Lobachevsky J. Math. 39 (6), 742–746 (2018).
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(Submitted by A. I. Aptekarev)
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Kalmetev, R.S., Orlov, Y.N. & Sakbaev, V.Z. Generalized Coherent States Representation. Lobachevskii J Math 42, 2608–2614 (2021). https://doi.org/10.1134/S1995080221110123
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DOI: https://doi.org/10.1134/S1995080221110123