The wave-corpuscle properties of microscopic particlesin the nonlinear quantum-mechanical systems

Xiao-feng Pang

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DOI: 10.4236/ns.2011.37083                

Abstract

We debate first the properties of quantum mechanics and its difficulties and the reasons resulting in these diffuculties and its direction of development. The fundamental principles of nonlinear quantum mechanics are proposed and established based on these shortcomings of quantum mechanics and real motions and interactions of microscopic particles and backgound field in physical systems. Subsequently, the motion laws and wave-corpuscle duality of microscopic particles described by nonlinear Schr?dinger equation are studied completely in detail using these elementary principles and theories. Concretely speaking, we investigate the wave-particle duality of the solution of the nonlinear Schr?dinger equation, the mechanism and rules of particle collision and the uncertainty relation of particle’s momentum and position, and so on. We obtained that the microscopic particles obey the classical rules of collision of motion and satisfy the minimum uncertainty relation of position and momentum, etc. From these studies we see clearly that the moved rules and features of microscopic particle in nonlinear quantum mechanics is different from those in linear quantum mechanics. Therefore, nolinear quantum mechanics is a necessary result of development of quantum mechanics and represents correctly the properties of microscopic particles in nonlinear systems, which can solve difficulties and problems disputed for about a century by scientists in linear quantum mechanics field.

Keywords

Microscopic Particle; NonlinearInteraction; Quantum Mechanics; Nonlinear Schrödinger Equation; Basic Principle; Nonlinear Theory; Wave-Particle Duality; Motion Rule

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Bohr, D. and Bub, J. (1966) A proposed solution of the measurement problem in quantum mechanics. Review of morden Physics, 6, 453-469. doi:10.1103/RevModPhys.38.453
[2]	Schr?dinger, E. (1935) Die gegenwartige situation in der quantenmechanik, Naturwissenschaften, 23, 807-812; 823-828; 844-849. doi:10.1007/BF01491891
[3]	Schr?dinger, E. (1935) The present situation in quantum mechanics, a translation of translation of Schrodinger. Proceedings of the American Philosophical Society, 124, 323-338.
[4]	Schr?dinger, E. (1926) An undulatory theory of the mechanics of atoms and molecules. Physical Review, 28, 1049-1070. doi:10.1103/PhysRev.28.1049
[5]	Heisenberg, W. Z. (1925) über die quantentheoretische umdeu- tung kinematischer und mechanischer beziehungen. Zeitschrift der Physik, 33, 879-893. doi:10.1007/BF01328377
[6]	Heisenberg, W. and Euler, H. (1936) Folgerungen aus der Diracschen Theorie des Positrons. Physics and Astronomy, 98, 714-732. doi:10.1007/BF01343663
[7]	Born, M. and Infeld, L. (1934) Foundations of the New Field Theory, Proceedings of the American Philosophical Society, 144, 425.
[8]	Dirac, P.A.M. (1948) Quantum Theory of Loca- lizable Dynamical Systems, Physical Review, 73, 1092. doi:10.1103/PhysRev.73.1092
[9]	Diner, S., Farque, D., Lochak, G., and Selleri, F. (1984) The wave-particle dualism. Riedel, Dordrecht.
[10]	Ferrero, M. and Van der Merwe, A. (1997) New developments on fundamental problems in quantum physics. Kluwer, Dordrecht.
[11]	Ferrero, M. and Van der Merwe, A. (1995) Fundamental problems in quantum physics. Kluwer, Dordrecht.
[12]	de Broglie, L., (1960) Nonlinear wave mechanics: A causal interpretation, Elsevier, Amsterdam.
[13]	de Broglie, L., (1955) Une interpretation nouvelle de la mechanique ondulatoire: est-elle possible?, Nuovo Cimento, 1, 37-50.
[14]	Bohm, D. A. (1952) Suggested interpretation of the quantum theory in terms of ‘hidden’ variables. Phys. Rev. 85, 166-180.
[15]	Potter, J. (1973) Quantum mechanics. North-Holland publishing Co. Amsterdam.
[16]	Jammer, M. (1989) The concettual development of quantum mechanics. Tomash Publishers, Los Angeles.
[17]	Einstein, A., Podolsky, B. and Rosen, N. (1935) The appearance of this work motivated the present – shall I say lecture or general confession? Physical. Review, 47, 777-780. doi:10.1103/PhysRev.47.777
[18]	Einstein, A.P., (1979) A centenary Volume. Harvard University Press, Cambridge.
[19]	Pang, X.F. (1985) Problems of nonlinear quantum mechanics. Sichuan Normal University Press, Chengdu.
[20]	Pang, X.F. (2008) The Schrodinger equation only descry- bes approximately the properties of motion of micro- scopic particles in quantum mechanics. Nature Sciences, 3, 29.
[21]	Pang, X.F. (1985) The fundamental principles and theory of nonlinear quantum mechanics. China Journal of Potential Science, 5, 16.
[22]	Pang, X.F. (1982) Macroscopic quantum mechanics. China Nature Journal, 4, 254.
[23]	Pang, X.F. (1986) Bose-condensed properties in supercon-ducors. Journal of Science Exploration, 4, 70.
[24]	Pang, X.F. (1991) The theory of nonlinear quantum mechanics: In research of new sciences, Science and Techbology Press, 16-20.
[25]	Pang, X.F. (2008) The wave-corpuscle duality of microscopic particles depicted by nonlinear Schrodinger equation. Physica B, 403, 4292-4300. doi:10.1016/j.physb.2008.09.031
[26]	Pang, X.F. (2008) Features and states of microscopic particles in nonlinear quantum–mechanics systems. Frontiers of physics in China, 3, 413.
[27]	Pang, X.F. (2005) Quantum mechanics in nonlinear systems. World Scientific Publishing Co., Singapore. doi:10.1142/9789812567789
[28]	Pang, X.F. (2009) Nonlinear quantum mechanics. china electronic industry press, Beijing.
[29]	Pang, X.F. (1994) The Theory of nonlinear quantum mechanics. Chinese Chongqing Press, Chongqing.
[30]	Pang, X.F. (2006) Establishment of nonlinear quantum mechanics. Research and Development and of World Science and Technology, 28, 11.
[31]	Pang, X.F. (2003) Rules of motion of microscopic particles in nonlinear systems. Research and Development and of World Science and Technology, 24, 54.
[32]	Pang, X.F. (2006) Features of motion of microscopic particles in nonlinear systems and nonlinear quantum mechanics in sciencetific proceding-physics and others. Atomic Energy Press, Beijing.
[33]	Parks, R. D. (1969) Superconductivity. Marcel, Dekker.
[34]	Josephson, D. A. (1965) Josephson, Supercurrents through barriers, Advanced Physics, 14, 39-451.
[35]	Suint-James, D. et al., (1966), Type-II superconductivity, Pergamon, Oxford.
[36]	Bardeen, L.N., Cooper L.N. and Schrieffer, J. R. (1957) Superconductivity theory. Physical Review, 108, 1175-1204. doi:10.1103/PhysRev.108.1175
[37]	Barenghi, C.F., Donnerlly, R.J. and Vinen, W.F. (2001) Quantized vortex dynamics and superfluid turbulence. Springer, Berlin. doi:10.1007/3-540-45542-6
[38]	Donnely, R.J. (1991) Quantum vortices in heliem II. Cambridge University Press, Cambridge.
[39]	Pang, X.F. (2003) Soliton physics. Sichuan Science and Technology Press, Chengdu.
[40]	Guo, B.L. and Pang, X.F. (1987) Solitons. Chinese Science Press, Beijing.
[41]	Zakharov, V.E. and Shabat, A.B. (1972) Exact theory of two-dimensional self-focusing and one-dimensional self- domulation of wave in nonlinear media. Soviet Physics JETP, 34, 62.
[42]	Zakharov, V.E. and Shabat, A.B. (1973) Interaction between solitons in a stable medium. Soviet Physics JETP, 37, 823
[43]	Lax, P.D., (1992) Integrals of nonlinear equations of evolution and solitary waves, Cambridge University Press, Cambridge, pp. 107-351
[44]	Pang, X.F. (2010) Collision properties of microscopic particles described by nonlinear Schrodinger equation. International Journal of Nonlinear science and numerical Simulation, 11, 1069-1075.
[45]	Stiefel, J. (1965) Einfuhrung in die numerische mathematik. Teubner Verlag, Stuttgart.
[46]	Atkinson, K.E. (1987) An Introdution to numerical analysis. Wiley, New York.
[47]	Pang, X.F. (2009) Uncertainty features of microscopic particles described by nonlinear Schr?dinger equation. Physica B, 405, 4327-4331. doi:10.1016/j.physb.2009.08.027
[48]	Glanber, R.J. (1963) Coherent and incoherent states of the radiation field. Physical Review, 13, 2766-2788. doi:10.1103/PhysRev.131.2766
[49]	Davydov, A. S. (1985) Solitons in molecular systems. D. Reidel Publishing, Dordrecht.
[50]	Pang, X.F. (2008) Properties of nonadiabatic quantum fluctuations for the strongly coupled electron-phonon system. Science in China Series G, 51, 225-336.
[51]	Pang, X.F. (1999) Influence of the soliton in anharmonic molecular crystals with temperature on Mossbauer effect. European Physical Journal B, 10, 415. doi:10.1007/s100510050871
[52]	Pang, X.F. (2001) The lifetime of the soliton in the improved Davydov model at the biological temperature 300K for protein molecules. Physics and Astronomy, 19, 297-316. doi:10.1007/s100510170339
[53]	Pang, X.F. (1990) The properties of collective excitation in organic protein molecular system. Journal of Physics: Condensed Matter, 2, 9541. doi:10.1088/0953-8984/2/48/008