[1] Hochstadt H. Integral Equations. New York: Wiley, 1973
[2] Fan H Y. Operator ordering in quantum optics theory and the development of Dira?s symbolic method. J Opt B: Quantum Semiclass Opt, 2003, 5: R1-R17
[3] Fan H Y, Tang X B. Operator Fredholm integration equation in intermediate coordinate-momentum representation and its analogue to thermo conduction equation. Commun Theor Phys, 2008, 49: 1169-1172
[4] Fan H Y, Lu H L, Fan Y. Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations. Ann Phys, 2006, 321: 480-494
[5] Erdelyi A. Higher Transcendental Functions: The Batemann Manuscript Project. New York: McGraw-Hill, 1953
[6] Namias V. The fractional order Fourier transform and its application to quantum mechanics. J Inst Math Its Appl, 1980, 25: 241-265
[7] Mendlovic D, Ozaktas H M. Fractional Fourier transforms and their optical implementation. J Optical Soc Am, 1993, 10(9): 1875-1881
[8] Bernado L M, Soares O D D. Fractional Fourier transforms and optical systems. Opt Commun, 1994, 110: 517-522
[9] Fan H Y, Xu X F. Talbot effect in a quadratic-index medium studied with two-variable Hermite polynomials and entangled states. Opt Lett, 2004, 29: 1048-1050
[10] Weyl H Z. Quantenmechanik und Gruppentheorie. Zeitschrift für Physik, 1927, 46: 1-46
[11] Weyl H. The Theory of Groups and Quantum Mechanics. Robertson H P (Translator). Montana: Kessinger Publishing, 2007
[12] Wigner E P. On the quantum correction for thermodynamic equilibrium. Phys Rev, 1932, 40: 749-759
[13] Fan H Y. Weyl ordering quantum mechanical operators by virtue of the IWWP technique. Phys A: Math Ge, 1992, 25: 3443-3447
[14] Fan H Y, Chen J H. EPR entangled state and generalized Bargmann transformation. Phys Lett A, 2002, 303: 311-317
[15] Fan H Y. General wigner transforms studied by virtue of Weyl ordering of the Wigner operator. Commun Theor Phys, 2003, 40: 409-414
[16] Chen J H, Fan H Y, Tang X B. Entanglement rule of Wigner operators at a beamsplitter. Int J Theor Phys, 2012, 51(1): 14-22
[17] Fan H Y, Wang Z. New integration transformation connecting coherent state and entangled state. Int J Theor Phys, 2014, 53: 964-970
[18] Fan H Y, Vanderlinde J. Similarity transformations in one- and two-mode Fock space. J Phys A, 1991, 24: 2529-2538
[19] Glauber R J. The quantum theory of optical coherence. Phys Rev, 1963, 130: 2529-2539
[20] Glauber R J. Coherent and incoherent states of the radiation field. Phys Rev, 1963, 131(6): 2766-2788
[21] Rempe G, Walther H, Klein N. Observation of quantum collapse and revival in a one-atom maser. Phys Rev Lett, 1987, 58: 353-356
[22] Schuster D I, HouckA A, Schreier J A, et al. Resolving photon number states in a superconducting circuit. Nature, 2007, 445: 515-518
[23] Jundt G, Robledo L, Högele A, Fält S, Imamo?lu A. Observation of dressed excitonic states in a single quantum dot. Phys Rev Lett, 2008, 100: 177401
[24] Huang J F, Law C K. Phase-kicked control of counter-rotating interactions in the quantum Rabi model. Phys Rev A, 2014, 89: 033827
[25] Majumdar A, Bajcsy M, Vu?kovi? J. Nonlinear temporal dynamics of a strongly coupled quantum-dot cavity system. Phys Rev A, 2012, 85: 033802
[26] Mehta C L. Diagonal coherent-state representation of quantum operators. Phys Rev Lett, 1967, 18: 752-754 |