The Difficulties of Quantum Mechanics and its Investigations of Development
microscopic particle, nonlinear systems, nonlinear interactions, quantum mechanics, localization, wavecorpuscle duality, motion rule, dynamic property
Abstract
When the states and properties of microscopic particles were described by linear SchrÖdinger equation the quantum mechanics had a lot of difficulties, which cause a centenary controversy in physics and have not a determinate conclusions till now. Thus we used a nonlinear SchrÖdinger equation to replace the linear SchrÖdinger equation and to depict and study in detail the states, properties and rules of motion of microscopic particles. Concretely speaking, we here investigated the properties and rules of wave-particle duality of microscopic particles and its stability, the invariances and conservation laws of motion of particles, the classical rule of motion, Hamiltonian principle of particle motion, corresponding Lagrangian and Hamilton equations for the microscopic particle, the mechanism and rules of particle collision in different nonlinear systems, the uncertainty relation of position and momentum of particles, the features of reflection and transmission of the particles at interfaces as well as the eigenvalue and eigenequations of the particles, and so on.
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D Bohr, J Bub (1935) Unknown Title. 48, 169.
E Schrödinger (1928) Collected paper on wave mechanics.
E Schrödinger (1935) Unknown Title. 31, 555.
W Heisenberg (1925) �ber quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen.. 33(1), 879-893.
W Heisenberg, H Euler (1936) Folgerungen aus der Diracschen Theorie des Positrons. 98(11-12), 714-732.
M Born, L Infeld (1934) Unknown Title. 144, 425.
P Dirac (1967) The Principles of Quantum Mechanics.
David Bohm (1952) A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II. 85(2), 180-193.
J Potter (1973) quantum mechanics.
M Jammer (1989) The concettual development of quantum mechanics.
J Meconnell (1958) Quantum particle dynamics By J. McConnell. Pp. xi + 252. North-Holland Publishing Co., Amsterdam. 1958. 40s. net. 18(71), 167.
L Roth, A Inomata (1986) Fundamental questions in quantum mechanics.
S Diner, D Farque, G Lochak, F Selleri (1984) The Wave-Particle Dualism.
F Selleri (1990) quantum daradoxes and physical reality.
M Ferrero, A Van Der Merwe (1997) New Developments on Fundamental Problems in Quantum Physics.
M Ferrero, A Van Der Merwe (1995) Fundamental Problems in Quantum Physics.
L De Broglie (1960) Nonlinear Wave Mechanics: A Causal Interpretation.
P Burt (1981) IUTAM symposium on nonlinear deformation waves. 8(6), 374.
Pang Xiao-Feng (1994) The theory of nonlinear quantum mechanics.
Pang Xiao-Feng (2003) Soliton Physics.
Go Bai, Pang Lin, Xiao-Feng (1987) Solitons.
Pang Xiao-Feng (2006) Unknown Title. 28, 11.
Pang Xiao-Feng (2003) Unknown Title. 24, 54.
Pang Xiao-Feng (1985) Unknown Title. 58, 334.
Pang Xiao-Feng (1985) Problems of Nonlinear Quantum Mechanics.
V Zakharov, A Shabat (1972) Unknown Title. 34, 62.
V Zakharov, A Shabat (1973) Unknown Title. 37, 823.
Pang Xiao-Feng, Chin (1981) Unknown Title. 4(3), 62.
Pang Xiao-Feng, Chin (1982) Rothschild rides again. 297(5864), 254-254.
Pang Xiao-Feng (1983) Unknown Title. 3, 17.
Pang Xiao-Feng, Chin (1985) Unknown Title. 5, 16.
Pang Xiao-Feng (1986) Unknown Title. 12, 31.
Pang Xiao-Feng (1986) Unknown Title. 4, 70.
Pang Xiao, -Feng, Cao Xianyu (2007) Unknown Title. 2, 42.
Pang Xiao-Feng (2008) Unknown Title. 6, 205.
H Chen, C Liu (1976) Unknown Title. 37, 693.
H Chen (1978) Unknown Title. 21, 377.
Pang Xiao-Feng (2003) Unknown Title. 236, 34.
Pang Xiao-Feng (2001) Unknown Title. 154, 138.
Pang Xiao-Feng (1990) The properties of the collective excitation in the organic protein molecular system. 2(48), 9541-9552.
Pang Xiao-Feng, H Miiller-Kirsten (2000) Unknown Title. 12, 885.
Pang Xiao, -Feng, Yuan Yuan-Ping (2003) Unknown Title. 373, 392.
C Desem, P Chu (1992) Soliton-soliton interactions. 107-151.
Benkui Tan, John Boyd (1998) Davydov soliton collisions. 240(6), 282-286.
Pang Xiao-Feng (2005) Unknown Title. 19, 3027.
Pang Xiao-Feng (2005) Unknown Title. 43, 367.
Pang Xiao-Feng, Liu Mei-Jie (2007) Properties of Soliton-Transported Bio-energy in α-Helix Protein Molecules with Three Channels. 48(2), 369-376.
David Aossey, Steven Skinner, Jamie Cooney, James Williams, Matthew Gavin, David Andersen, Karl Lonngren (1992) Properties of soliton-soliton collisions. 45(4), 2606-2610.
R Thurston, A Weiner (1991) Unknown Title. 8, 471.
Jamie Cooney, Matthew Gavin, James Williams, David Aossey, Karl Lonngren (1991) Soliton propagation, collision, and reflection at a sheath in a positive ion-negative ion plasma. 3(12), 3277-3285.
N Zabuasky, M (1965) Unknown Title. 15, 240.
H Ikezl, R Taylor, D Baker (1970) Unknown Title. 25, 11.
G Lamb (1980) Elements of soliton theory. 118.
A Davydov (1985) Solitons in Molecular Systems.
Pang Xiao-Feng (2000) Improvement of the Davydov theory of bioenergy transport in protein molecular systems. 62(5), 6989-6998.
Pang Xiao-Feng (2001) Unknown Title. 19, 297.
Pang Xiao-Feng (1999) Unknown Title. 10, 415.
Pang Xiao-Feng (1999) Unknown Title. 259, 466.
Pang Xiao-Feng (2001) Unknown Title. 62, 491.
Pang Xiao-Feng (2008) Unknown Title. 51, 225.
J Bardeen, L Cooper, J Schrieffer (1957) Theory of Superconductivity. 108(5), 1175-1204.
Y Lai, H Haus (1989) Quantum theory of solitons in optical fibers. II. Exact solution. 40(2), 854-866.
F Kartner, L Boivin (1996) Unknown Title. 53, 454.
C Sulem, P Sulem (1999) The Nonlinrar SchrÖdinger Equation: Self-focusing and Wave Collapse.
C Desem, P Chu (1987) Soliton interaction in the presence of loss and periodic amplification in optical fibers. 12(5), 349.
K Lonngren (1983) Soliton experiments in plasmas. 25(9), 943-982.
K Lonngren, D Andersen, J Cooney (1991) Unknown Title. 156, 441.
A Aceves, J Mononey, A Newell (1989) Unknown Title. 39, 1809-1839.
K Lonngren, A Scott (1978) Solitons in Action. 15.
A Scott, J Eilbeck (1986) The quantized discrete self-trapping equation. 119(2), 60-64.
A Scott, J Eilbeck (1986) On the CH stretch overtones of benzene. 132(1), 23-28.
A Scott, P Lomdahl, J Eilbeck (1985) Between the local-mode and normal-mode limits. 113(1), 29-36.
Pang Xiao-Feng (1994) Unknown Title. 43, 1987.
Pang Xiao-Feng, Chin (1995) Contents: Chin. J. Chem. 8/2007. 25(8), 1055-1062.
Pang Xiao-Feng, Chen Xiang-Rong (2000) Nonlinearly vibrational energy-spectra of molecular crystals. 9(2), 108-112.
Pang Xiao-Feng, X Chen (2001) Unknown Title. 35, 313.
Pang Xiao-Feng, X Chen (2001) The Features of Infrared Absorption of the Protein Molecules in the Living System. 35(6), 763-768.
Pang Xiao-Feng, X Chen (2001) Unknown Title. 62, 793.
Pang Xiao-Feng, H Zhang (2006) Unknown Title. 20, 1923.
Pang Xiao-Feng, X Chen (2006) Unknown Title. 20, 2505.
Junkichi Satsuma, Nobuo Yajima (1974) B. Initial Value Problems of One-Dimensional Self-Modulation of Nonlinear Waves in Dispersive Media. 55, 284-306.
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2016-11-28
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