Abstract
In the paper we construct a new set of coherent states for a deformed Hamiltonian of the harmonic oscillator, previously introduced by Beckers, Debergh, and Szafraniec, which we have called the BDS-Hamiltonian. This Hamiltonian depends on the new creation operator a λ +, i.e. the usual creation operator displaced with the real quantity λ. In order to construct the coherent states, we use a new measure in the Hilbert space of the Hamiltonian eigenstates, in fact we change the inner product. This ansatz assures that the set of eigenstates be orthonormalized and complete. In the new inner product space the BDS-Hamiltonian is self-adjoint. Using these coherent states, we construct the corresponding density operator and we find the P-distribution function of the unnormalized density operator of the BDS-Hamiltonian. Also, we calculate some thermal averages related to the BDS-oscillators system which obey the quantum canonical distribution conditions.
Similar content being viewed by others
References
R.J. Glauber: Phys. Rev. 131 (1963) 2766.
J.R. Klauder: J. Math. Phys. 4 (1963) 1055; 1058.
J.R. Klauder and B.S. Skagerstam: Coherent States, World Scientific, Singapore, 1985.
A.M. Perelomov: Generalized Coherent States and Their Applications, Springer, Berlin, 1986.
D. Stoler: Phys. Rev. D 1 (1970) 3217; 4 (1971) 1925
J. Beckers, N. Debergh, and F.H. Szafraniec: Phys. Lett. A 243 (1998) 256.
D. Popov: Int. J. Theor. Phys. 40 (2001) 861.
A. Messiah: Quantum Mechanics, North Holland, Amsterdam, 1968.
S.T. Ali, J.-P. Antoine, J.-P. Gazeau, and U. A. Mueller: Rev. Math. Phys. 7 (1995) 1013.
F.E. Schroeck, Jr.: Quantum Mechanics on Phase Space, Kluwer, Dordrecht, 1996.
A. Isar: Helv. Phys. Acta 67 (1994) 436.
R. Kubo: Statistical Mechanics, North Holland, Amsterdam, 1965.
F. Bloch: Z. Phys. 74 (1932) 295.
I.A. Vakarchuk: Teor. Mat. Fiz. 35 (1978) 76.
D.F. Walls and G.J. Milburn: Quantum Optics, Springer, Berlin, 1994.
P. Marian and T.A. Marian: Phys. Rev. A 47 (1993) 4474.
A. Wuensche: J. Opt. B: Quantum Semiclass. Opt. 1 (1999) 264.
J. Peřina: Quantum Statistics of Linear and Nonlinear Optical Phenomena, Reidel, Dordrecht–Boston–Lancaster, 1984.
G. Adam: J. Mod. Opt. 42 (1995) 1311.
D. Popov: Czech. J. Phys. 49 (1999) 1121.
I.S. Gradshteyn and I.M. Ryzhyk: Tables of Sums, Series, Products and Integrals, 4th ed., Nauka, Moscow, 1963 (in Russian).
G. Lévai: J. Phys. A: Math. Gen. 27 (1994) 3809.
J. Beckers, N. Debergh, J.F. Cariñena, and G. Marmo: Mod. Phys. Lett. A 16 (2001) 91.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Popov, D. New Coherent States for the BDS-Hamiltonian. Czechoslovak Journal of Physics 52, 993–1010 (2002). https://doi.org/10.1023/A:1020543814491
Issue Date:
DOI: https://doi.org/10.1023/A:1020543814491