All these paradoxes that quantum mechanics imposed, along with the wave-corpuscle duality, determined a new approach in physics, mathematics, and in the scientific approach in general.
From the perspective offered to us nowadays by the evolution of scientific knowledge, the insistence on the wave-corpuscle duality seems to be hard to understand, as it aroused so many interpretations, thus evading the problem of information.
Therefore, we can understand the paradoxical aspects offered by the slit experiment, and, generally, the wave-corpuscle duality, which generated so many controversies.
These features of microscopic particles are not only incompatible with de Broglie relation of wave-corpuscle duality of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and Davisson and Germer's experimental result of electron diffraction on double seam in 1927 [10-13] but also contradictory with regard to the traditional concept of particles [14-16].
Thus the microscopic particles have a wave-corpuscle duality in such a case.
1.1 The Wave-Corpuscle Duality of Solutions of Nonlinear Schrodinger Equation
Thus we believe that the microscopic particles described by nonlinear quantum mechanics have simultaneously a wave-corpuscle duality. Equations (14)-(16) and Figure 1(a) are just the most beautiful and perfect representation of this property, which consists also of de Broglie relation, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], wave-corpuscle duality and Davisson and Germer's experimental result of electron diffraction on double seam in 1927 as well as the traditional concept of particles in physics [10-13].
1.2 The Wave-Corpuscle Duality of Solution of the Nonlinear Schrodinger Equation with Different Potentials
We can verify that the nature of wave-corpuscle duality of microscopic particles is not changed when varying the externally applied potentials.
Therefore we can determine that the microscopic particles described by these dynamic equations still possess a wave-corpuscle duality as shown in Figure 1, although they are acted by different external potentials.
Nouailhat covers the basic facts from wave-corpuscle duality
and probability in the quantum world to the work of electrons and photons, the functionality of matter at the molecule level, quantum boxes, observing with photons and electrons, and applications such as nuclear magnetic resonance.
Ten chapters cover macroscopic quantum effects, a proposed theory of nonlinear quantum mechanics, the wave-corpuscle duality
of particles in nonlinear systems, mechanisms of nonlinear interactions and their relations to localization of particles, comparative features of nonlinear and linear quantum mechanical theories, methods of solving nonlinear quantum mechanical systems, dynamic properties of microscopic particles in different nonlinear systems, and applications in the various physical systems mentioned above.