scholarly journals Stochastic reduction in nonlinear quantum mechanics

2002 ◽  
Vol 458 (2021) ◽  
pp. 1117-1127 ◽  
Author(s):  
Dorje C. Brody ◽  
Lane P. Hughston
Keyword(s):  
Quantum Mechanics ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation

2014 ◽  
Vol 5 (3) ◽  
pp. 871-981 ◽  
Author(s):  
Pang Xiao Feng
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Lagrange Equation ◽  
Minimum Principle ◽  
Superposition Principle ◽  
Type Equation ◽  
Experimental Results ◽  
Traditional Concept ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary wave’s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear Schrödinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

Nonlinear quantum mechanics in a q-deformed Hilbert space

2019 ◽  
Vol 383 (23) ◽  
pp. 2729-2738 ◽  
Author(s):  
Bruno G. da Costa ◽  
Ernesto P. Borges
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

Stationary and uniformly accelerated states in nonlinear quantum mechanics

2014 ◽  
Vol 90 (6) ◽  
Author(s):  
A. R. Plastino ◽  
A. M. C. Souza ◽  
F. D. Nobre ◽  
C. Tsallis
Keyword(s):  
Quantum Mechanics ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

scholarly journals Classical Mechanics as Nonlinear Quantum Mechanics

2007 ◽  
Author(s):  
Hrvoje Nikolić ◽  
Guillaume Adenier ◽  
Andrei Yu. Khrennikov ◽  
Pekka Lahti ◽  
Vladimir I. Man'ko ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

NONLINEAR QUANTUM MECHANICS WITH NONCLASSICAL GRAVITATIONAL SELF-INTERACTION II: NONSTATIONARY SITUATION

1993 ◽  
Vol 08 (16) ◽  
pp. 2683-2707 ◽  
Author(s):  
A. D. POPOVA ◽  
A. N. PETROV
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Variational Principles ◽  
Gravitational Interaction ◽  
Classical Field Theory ◽  
Classical Field ◽  
Stationary Case ◽  
Self Consistent ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

Quantum mechanics (first quantization) with self-consistent gravitational interaction, previously constructed for the stationary case, is extended to the general case. The two requirements for such a theory are realized: to obtain the theory maximally resembling a classical field theory and to achieve the invariance of the theory under the rescaling transformations of a wave function. The construction is not trivial, because it rejects the variational principles of extremality of any action and involves some principles of smoothed extremality which give relevant equations.

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