1-3 纠缠态(Entangled state)解析
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全书中的参考文献-修改版前言文献:[1] Dirac P A M. Recollections of an exciting area: History of 20th Century Physics [M]. NewY ork: Academic Press, 1977.[2] Dirac P A M. The Principles of Quantum Mechanics [M]. Oxford: Clarendon Press, 1930.[3] FAN H Y. Recent Development of Dirac?s Representation theor y. In: Feng D H, Klauder J R,Strayer M R. Coherent states[M]. New Y ork: Academic Press, 1994. p153.[4] FAN H Y, ZAIDI H R, KLAUDER J R. New approach for calculating the normally ordered form of squeeze operators[J]. Physical review, 1987, D35 (6):1831--1834.[5] FAN H Y, ZAIDI H R. Squeezing and frequency jump of a harmonic oscillator[J]. PhysicsReview, 1988, A 37(8) : 2985-2988.[6] FAN H Y, V ANDERLINDE J, Mapping of classical canonical transformations to quantumunitary operators[J].Physical review, 1989, A39 (6):2987-2993; Squeezed-state wave functions and their relation to classical phase-space maps[J].A40 (8):4785-4788; A39 (3): 1552-1555; FAN Y.EPR Entangled States for Bipartite Kinematics and New Bosonic Representation of SU(2) Algebra [J]. Physical review, 1996, A54 (1):958-960.[7] FAN H Y. Squeezed states: Operators for two types of one- and two-mode squeezing transformations [J]. Physical review, 1990. A41(3): 1526-1532.[8] FAN H Y, RUAN T N. Sci. Sin., 1984, A27: 392; Some newapplications of the coherentstates[J]. Communications of Theoretical Physics, 1983, 2 (4):1289.[9] FAN H Y, XU Z H, Symplectic transformations in the n-mode coherent-state representationusing integration within an ordered product of operators[J]. Physical review. 1994, A 50 (4): 2921--2925; FAN H Y, V ANDERLINDE J. 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Recollections of an exciting area: History of 20th Century Physics [M]. NewY ork: Academic Press, 1977, 109.[3] DIRAC P A M. Directions in Physics [M]. New Y ork: John Wiley, 1978.[4] DIRAC P A M. The Physicist?s conception of Nature [M]. New Y ork: Mehra, 1973.[5] LOUISELL W H. Quantum Statistical Properties of Radiation [M]. New Y ork: Wiley, 1973.[6] WICK G. The Evaluation of the Collision Matrix [J]. Physical review, 1950, 80: 268--272.[7] BOGOLYUBOV N N. Lectures on Quantum Statistics (V ol.1)[M]. New Y ork: Gordon andBreach ,1987.[8] Klauder J R and Skagerstam B S. Coherent States. Singapore: World Scientific Publishing Co.,1985[9] GLAUBER R J. The Quantum Theory of Optical Coherence [J]. Physical review, 1963, 130: 2529-2539 ;Coherent and Incoherent States of the Radiation Field[J]. Physical review, 131:2766-2788.[10] WEYL H Z.Quantenmechanik und Gruppentheorie[J]. Zeitschrift für Physik, 1927, 46: 1-46.[11] WIGNER E, On the Quantum Correction For Thermodynamic Equilibrium[J]. Physical review, 1932, 40: 749--759.[12]FAN H Y, WANG W Q. Coherent-Entangled State in Three-Mode and Its Applications [J]. Communications of Theoretical Physics, 2006, 46: 975.[13] W ALLS D F , G. J. Milburn. Quantum Optics [M], New Y ork: Springer- V erlag, 1995.[14] FAN H Y, LIU S G, New Approach for Finding Multipartite Entangled State Representations via the IWOP Technique [J].International Journal of Modern Physics A, in press[15] FAN H Y, LU H L. New two-mode coherent-entangled state and its application[J]. Journal of Physics A: Mathematical and General, 2004, 37:10993-11001.第二章文献:[1] FAN H Y, FAN Y. New Eigenmodes of Propagation in Quadratic Graded Index Media and Complex Fractional Fourier Transform [J] Communications of Theoretical Physics, 2003, 39: 97–100.[2] NAMIAS V. The fractional order Fourier transform and its application to quantummechanics[J]. J. Inst. Maths Applics, 1980, 25:241-265.[3] MCBRIDE A C, KERR F H. 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Physical Review Letters, 1967, 18: 752--754.[15] WIGNER E,On the Quantum Correction For Thermodynamic Equilibrium [J].Physical Review, 1932, 40: 749--759.[16] HELGASON S. The Randon Transform [M].Boston(Massachusetts): Birkhauser, 1980;Radon transform and pattern functions in quantum tomography[J]. Journal WUNSCHE A.of Modern Optics, 1997,44(11-12): 2293-2331.第三章文献:[1] 范洪义,从量子力学到量子光学——数理进展[M],上海:上海交通大学出版社,2005.[2] FAN H Y, LU H L, New two-mode coherent-entangled state and its application[J]. Journal of Physics A: Mathematical and General, 2004, 37: 10993-11001; FAN H Y, TANG X B. New squeezing operator derived using the bipartite coherent entangled state representation[J]. Journal of Optics B: Quantum and Semiclassical Optics, 2005, 7: S765-S768.[3] FAN H Y, JIANG N Q. Special Two-Mode Unitary Transform and Maximum Entanglement State for Four Wave Mixing [J]. Physica Scripta, 2005, 71: 277—279.[4] DA VYDOV A S. 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Special Functions [M], 2ed, Meteorology Publishing Press, (2002) p.80.[17] FAN H Y. Entangled State Representation for Hamiltonian Operator of Quantum Pendulum[J]. Communications in Theoretical Physics, 2003, 40: 157–160.[18] MANDL L, WOLF E. Optical Coherence and Quantum Optics [M], Cambridge, 1996.[19] SCHWINGER J. Quantum Theory of Angular Momentum [M], New Y ork:Academic Press, 1965.[20] FAN H Y, W ANG J S. Angular Momentum Phase State Representation for QuantumPendulum[J]. Communications in Theoretical Physics, 2005, 43: 611–614.[21] MA THEWS J, W ALKER R L. Mathematical Methods of Physics [M], London:TheBen-jamin/Cumming Pub. Com. 1970.[22] NAMIAS V. The fractional order fourier transform and its applications to quantum mechanics[J].J. Inst. Maths. Applics, 1980, 25: 241-265.[23] GOODMAN J M. Introduction to Fourier Optics [M]. New York:McGraw-Hill , 1968.[24] FAN H Y, LI C, LIU Q Y, et al. Path Integral Formalism for Nondegenerate ParametricAmplifiers in Entangled State Representation[J]. Communications in Theoretical Physics, 2005, 43: 998–1002.[25] GRADSHTEYN I S, RYZHIK I M. Table of integrals[M], series and products.NewY ork :Academic press.1980, page844.[26] MAGNUS W, et al, Formulas and Theorems for the Special Functions of MathematicalPhysics [M], 3rd ed. Berlin:Springer, 1966 .[27] MARLAN O S, ZUBAIRY M S. Quantum Optics [M], NewY ork: Cambridge UniversityPress, 1997.[28] TAKAHASHI Y, UMEZAWA H. Thermo field dynamics[J].Collecive Phenomena, 2(1975),55-80.[29] FAN H Y, Application of Weyl-Wigner method in calculating thermal averages[J].Communications in Theoretical Physics, 1991, 16(1): 123-128.[30] DRUMMOND P D, GARDINER C W. Generalised P-representations in quantum optics[J]. Journal of Physics A: Math, 1980, 13: 2353-2368.第五章文献:[1] FAN H Y, W ANG Y. Generating Generalized Bessel Equations by V irtue of Bose OperatorAlgebra and Entangled State Representations[J]. Communications in Theoretical Physics, 2006, 45:71-74.[2] W A TSON G N. Theory of Bessel Functions, Cambridge [M], 1944; WHITTAKER E T,WA TSON G N. Modern Analysis [M], 4thed. Cambridge, 1952.[3] ARFKEN G B, WEBER H J. Mathematical methods for Physicists[[M], 5th Edition, AharcourtScience and Technology Company, 2001.[4] See,e.g., SNEDDON I N. The Use of Integral Transforms [M], New Y ork: McGraw-Hill, 1975;MAGNUS W, et al. Formulas and Theorems for the Special Functions of Mathematical Physics [M], 3rd Edition, Springer V erlag, 1996.[5] W A TSON G N. Theory of Bessel Functions [M], Cambridge, 1944; WHITTAKER E T,WA TSON G N. Modern Analysis [M], 4th ed. Cambridge, 1952.[6] LOUDON R, KNIGHT P L. Squeezed Light[J]. Journal of Modern Optics, 1987, 34: 709-759.[7] ARFKEN G B, WEBER H J. Mathematical Methods for Physicists [M], 5th Edition, London:Harcourt/Academic Press Science and Technology Company, 2001.[8] FAN H Y, Hankel transform as a transform between two entangled state representations[J].Physics Letters, 2003, A313: 343-350; FAN H Y, HUI Z, FAN Y, New applications of <η | representation in obtaining charge raising and lowering operators[J]. Physics Letters, 1999, A 254; 137-140.[9] VOGEL K, RISKEN H.Determination of quasiprobability distributions in terms of probabilitydistributions for the rotated quadrature phase[J]. Physical Review,1989, A40: 2847-2849.[10] SMITHEY D T, BECK T, RAY M G, et al.Measurement of the Wigner distribution and thedensity matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum[J]. Physical Review Letters, 1993, 70:1244-1247.第六章文献:[1] FAN H Y, Y ANG Y L. Weyl ordering, normally ordering of Husimi operator as the squeezedcoherent state projector and its applications[J]. Physics Letters, 2006, A353: 439-445;FAN H Y, QIN G. Entangled Husimi operator as a pure state density matrix of two-mode squeezed coherent state[J]. Physics Letters, 2006, A358: 203-210.[2] WIGNER E. On the Quantum Correction For Thermodynamic Equilibrium[J]. PhysicalReview, 1932, 40: 749-759.[3] HUSIMI K. Some Formal Properties of the Density Matrix[J]. Proc. Phys. Math. Soc. Japan,1940, 22: 264-314.[4] HELGASON S. The Randon Transform[M]. Boston(Massachusetts): Birkhauser, 1980;WUNSCHE A. Radon transform and pattern functions in quantum tomography[J].Journal of Modern Optics, 1997, 44(11-12): 2293-2331.[5] 范洪义. 量子力学纠缠态表象及应用[M]. 上海:上海交通大学出版社,2001.[6] 范洪义. 量子力学表象与变换论——狄拉克符号法进展[M]. 上海:上海科学技术出版社,1997.[7] COHEN L. Generalized phase-space distribution functions[J]. Journal of Mathematical Physics, 1966, 7: 781-786.第七章文献:[1] FAN H Y, LIANG F. Normal ordering expansion of n-dimensional radial coordinate operatorsgained by virtue of the IWOP technique[J]. Journal of Physics A: Mathematical and General, 2003, 36: 1531–1536.[2] WHITTAKER E T, WA TSON G N. A Course of Modern Analysis [M] 4th ed Cambridge:Cambridge University Press, 1927, p366.[3] W AN Z X, GUO D R.An Introduction to Special Function [M], Beijing: Peking UniversityPress, 2000, p290.[4] LOUDON R, KNIGHT P L. Squeezed Light[J] Journal of Modern Optics, 1987, 34(6-7):709-759; DODONOV V V. …Nonclassical? states in quantum optics: a …squeezed? review of the first 75 years[J]. Journal of Optics B: Quantum Semiclassical Optics, 2002, 4:R1-R33. [5] BRACEWELL R.The Fourier Transform and Its Applications [M], 3rd ed, New Y ork:McGraw-Hill, 1999, p267—272,.[6] PAPOULIS A. The Fourier Integral and Its Applications [M],New Y ork: McGraw-Hill, pp.198—201, 1962.[7] GRADSHTEYN I S, RYZHIK I M. Table of Integrals, Series and Products [M], New Y ork:Academic Press , 1980.[8] FAN H Y, TANG X B. New squeezing operator derived using the bipartite coherent entangledstate representation[J]. Journal of Optics B: Quantum Semic lassical Optics, 2005, 7:S765–S768.[9] FAN H Y, LU H L. New two-mode coherent-entangled state and its application[J]. Journal ofPhysics A: Mathematical and General, 2004, 37: 10993-11001.第八章文献:[1] FAN H Y, Weyl-Ordered Operator Moyal Bracket by Virtue of Method of Integral Within anWeyl Ordered Product of Operators[J]. Communications in Theoretical Physics, 2006, 45: 245–248.[2] MEHTA C L. Diagonal Coherent-State Representation of Quantum Operators[J]. PhysicalReview Letters, 1967, 18: 752-754.[3] 范洪义. 量子力学表象与变换论——狄拉克符号法进展[M]. 上海:上海科学技术出版社,1997.[4] FAN H Y, Time evolution of the Wigner function in the entangled-state representation[J].Physical Review, 2002, A65: 064102-064105.[5] SONG F J, JUTAMULIA S. Modern Optical Information Processing [M], Beijing:PekingUniversity Press, 1999.[6] FAN H Y, WUNSCHE A. Design of squeezing[J]. Journal of Optics B: Quantum SemiclassicalOptics, 2000, 2: 464-469.第九章文献:[1] KLITZING K VON, DORDA G G, PEPPER M. New Method for High-AccuracyDetermination of the Fine-Structure Constant Based on Quantized Hall Resistance[J].Physical Review Letters, 1980, 45: 494-497.[2] TSUI D C, STORMERANG H L, GOSSARD A C. Two-Dimensional Magnetotransport in theExtreme Quantum Limit[J].Physical Review Letters, 1982, 48: 1559-1562; LAUGHLIN R B.Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations[J].Physical Review Letters, 1983, 50: 1395-1398; Chakravarty S, Halperin B I and Nelson D R. Low-temperature behavior of two-dimensional quantum antiferromagnets[J]. Physical Review Letters, 1988, 60: 1057-1060; LAUGHLIN R B. The Relationship Between High-Temperature Superconductivity and the Fractional Quantum Hall Effect[J]. Science, 1988, 242: 525-533; LAUGHLIN R B. Nobel Lecture: Fractional quantization[J]. Reviews of Modern Physics, 1999, 71: 863-874.[3] LANDAU L D.Diamagnetismus der Metalle[J]. Zeitschrift fur Physik, 1930, 64: 629-637.[4] FAN H Y, New state vector representation for the two-dimensional harmonic oscillator [J].Physical Letters, 1987, A 126 (3): 145-149.[5] JOHNSONANG M H, LIPPMANN B A. Motion in a Constant Magnetic Field[J]. PhysicalReview, 1946, 76: 828-832.[6] LIFSHITZ E M, PITAEVSKII L P. Statistical Physics: Part2 [M],Oxford: Pergamon Press,1980; FERRARI R. Two-dimensional electrons in a strong magnetic field: A basis for single-particle states[J].Physical Review, 1990, B42: 4598-4609.[7] SERIMAA O T, JA V ANAINENAND J, V ARRO S. Gauge-independent Wigner functions:General formulation[J].Physical Review, 1986, A 33: 2913-2927.[8] FAN H Y, Y ANG Z S, LIU N L. A kq-analogue representation for a Bloch electron in auniform magnetic field[J]. Physical Letters, 1998, A 249: 133-139.[9] KLAUDER J R, SKARGERSTAM B S. Coherent States [M], Singapore:World Scientific,1985 ;FAN H Y, FAN Y. Weyl ordering for entangled state representation[J]. International Journal of Modern Physics, 2002, A17: 701-708; FAN H Y, FAN Y. Derivation of squeezed states via Weyl ordering approach[J]. Modern Physics Letter, 1997, A12: 2325-2329; FAN H Y. Weyl-ordered Polynomials Studied by Virtue of the IWWOP Technique[J]. Modern Physics Letter, 2000, A15: 2297-2303.[10] FAN H Y, XU X F, Energy Shift Caused by Non-isotropy of 2-Dimensional AnisotropicQuantum Dot in Presence of Uniform Magnetic Field[J]. Communications in Theoretical Physics, 2005, 44: 615–618.[11] FAN H Y, A New Differential Formula About Product of Polynomials and Its Application inMulti-electron State Physics[J]. Communications in Theoretical Physics, 2006, 46: 419–422.[12] LAUGHLIN R B. Anomalous Quantum Hall Effect: AnIncompressible Quantum Fluid withFractionally Charged Excitations[J]. Physical Review Letters, 1983, 50:1395-1398;Chakravarty S, Halperin B I and Nelson D R. Low-temperature behavior of two-dimensional quantum antiferromagnets[J]. Physical Review Letters, 1988, 60: 1057-1060; LAUGHLIN RB. The Relationship Between High-Temperature Superconductivity and the FractionalQuantum Hall Effect[J]. Science, 1988, 242: 525-533; LAUGHLIN R B. Nobel Lecture: Fractional quantization[J]. Reviews of Modern Physics, 1999, 71: 863-874; TUI D C, STORMER H L, GOSSARD A C. Two-Dimensional Magnetotransport in the Extreme Quantum Limit[J].Physical Review Letters, 1982, 48: 1559-1562; K.von Klitzing, DORDA G, PEPPER M. New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance[J].Physical Review Letters, 1980, 45: 494-497.[13] CHARKRABORTY T, P. Pietil?inen, The Quantum Hall Effects: ractional and Integral [M],2nd ed. Berlin: Springer-V erlag, 1995; PRANGE R E, GIRVIN S M. Quantum Hall Effects [M], New Y ork: Springer, 1990; STONE M. Quantum Hall Effects [M], Singapore: World Scientific, 1992.第十章文献:[1] LOUISELL W H. 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微观物态及特性The microscopic state and its characteristics作者:罗华林作者单位:陕西省化肥厂退休工人。
地址:陕西省渭南市华县瓜坡镇陕化家属区。
邮编:714100关键词:微观物态,量子,基本粒子,媒介子,强力,弱力,电磁力,万有引力,光子,纠缠态(micro state , quantum , elementary , mediated meson ,brute force , weak force , electromagnetic force ,universal gravitation , photon , entangled state )摘要本文是一部,以真空中媒介子为真实客体,而建立的物质运动与物质结构力学新理论来描述解释微观物态特征性质的文章。
文章分篇着重地论述时间、空间特性、真空中物态分布特性、媒介子的作用过程和它的能量信号传递特性、粒子的自旋和纠缠态、普朗克常数的意义、光的波粒二相性的本质、物质波、带电粒子的运动与辐射、基本粒子和物质结构与构架力的作用、黑洞、物质湮灭与能量、质量和万有引力的本质。
文章在前言中用充分地事实理由说明,现有的物理理论存在问题。
包括经典的牛顿力学、相对论和量子力学以实际客观的必要提出了新物理理论新概念,来描述解释微观物态和宏观现象的关系。
文章在结束语中,总结了这一理论的系统性和贯穿性及普适性。
从科学的历史发展观来看,一切新的正确的东西都是在不断地修正错误来完善正确。
这是一个必然的自然规律。
正确的理论必是具有普适性和指导性。
科学无止境,理论也必将发展。
前言大千世界林林总总的宏观之物,大到星体,小到生命细胞,分子,原子,它们形形色色千奇怪的表现,使人难以想象大自然为何竟是如此之妙。
然而能造成如此之妙境的原因却是微小世界的基本粒子所致。
微观物态是人们感到非常神秘的世界。
自从人们知道了物质是由晶体和分子构成之时,人们就发现了很多在宏观所见不到的现象。