The diffraction pattern by double slit is studied by incoming Gaus-sian wave packet subjected to scattering interaction with the wall and a truncation assumption when crossing the slits. Explicit results are valid for sufficiently smooth scattering amplitude. They concern large and narrow aperture of the incoming wave packet. For wave packet localized in spatial region smaller then the aperture of the slits there is no diffraction and the particle behaves classically. For wave packet peaked in the momentum probability distribution there are maxima, superimposed to the canonical diffraction pattern, in correspondence to the edges of the slits. Previous similar results are generalized and improved.
The diffraction pattern by double slit is studied by incoming Gaus-sian wave packet subjected to scattering interaction with the wall and a truncation assumption when crossing the slits. Explicit results are valid for sufficiently smooth scattering amplitude. They concern large and narrow aperture of the incoming wave packet. For wave packet localized in spatial region smaller then the aperture of the slits there is no diffraction and the particle behaves classically. For wave packet peaked in the momentum probability distribution there are maxima, superimposed to the canonical diffraction pattern, in correspondence to the edges of the slits. Previous similar results are generalized and improved.
Abstract The goal of this paper is to study double-slit diffraction at the nanometric scale. We treat the time evolution of a Gaussian wave packet in quantum mechanics traveling until it reaches a double-slit wall. A detailed investigation and analysis of the diffraction phenomenon and its progress is developed by numerically solving the Schrödinger equation. This is written using a potential intended to model the wall. It is solved by using finite differences in the time domain method, so that the probability amplitude, ψ , is obtained as a function of the spatial coordinates at discretized times. Then, the probability density, ρ , is found in a straightforward way and used to plot graphics or make videos. Furthermore, the time evolution of the wave packet is registered at several fixed points to acquire local information. Fourier transforms are calculated to complement the knowledge obtained. Students interested in didactic approaches, or in applications for nanodevices, could find interest in this approach.
Scattering through a double slit potential is one of the most fundamental problems in quantum mechanics. It is well understood that due to the superposition of amplitudes, one observes a spatial interference pattern in the scattered wavefunction reflecting the superposition of amplitudes coming from both slits. However, the effect of the double slit on the mean time it takes to traverse the slit has not been considered previously. Using a transition path time formalism, we show that when a single Gaussian wavepacket is scattered through a double slit potential, one finds not only oscillations in the scattered density resulting from the spatial interference created by the splitting of the wavepacket but also an oscillatory pattern in the mean scattering time. Long times are associated with low values of a suitably defined momentum, and short times with higher values. The double slit thus serves as a momentum filtering device. We also find an interference pattern in the time averaged momentum weak value profile of the scattered particle implying that the double slit also acts as a weak momentum filter. These results not only demonstrate the value of considering transition path time distributions in their quantum mechanical context but also present a challenge to semiclassical approximations-can they account for temporal interference?
The double slit has been extended to the cross double slits. The universal phenomena that, in classical double slit wave experiments, the nature and the characteristics of the patterns are distance-dependent. The pattern evolutions have been shown. In this article, we extend the single slit to the cross single slit, e.g., single slits crossing single slits, single slit crossing double slit, etc. Then we experimentally show that, within macroscopic distances from diaphragm, patterns are non-diffraction and gradually evolve to the diffraction patterns near the screen in the same single slit/cross single slit experiment. L: mm Tilt single slit crossing single slit Single slit crossing single slit 4 single slits crossing Single slit crossing Ring Single slit crossing double slit 0* 10 50 110 1100 Challenge is to interpret consistently the non-diffraction patterns, the diffraction patterns, and the pattern evolution phenomena.
The double slit has been extended to the cross double slits. The universal phenomena that, in classical double slit wave experiments, the nature and the characteristics of the patterns are distance-dependent. The pattern evolutions have been shown. In this article, we extend the single slit to the cross single slit, e.g., single slits crossing single slits, single slit crossing double slit, etc. Then we experimentally show that, within macroscopic distances from diaphragm, patterns are non-diffraction and gradually evolve to the diffraction patterns near the screen in the same single slit/cross single slit experiment. L: mm Tilt single slit crossing single slit Single slit crossing single slit 4 single slits crossing Single slit crossing Ring Single slit crossing double slit 0* 10 50 110 1100 Challenge is to interpret consistently the non-diffraction patterns, the diffraction patterns, and the pattern evolution phenomena.
The mainstream quantum mechanics uses “probability wave superposition and single-electron self-interference” to explain electron single-slit and double-slit diffraction. This theory deviates from the essential nature of real particle interactions and has fundamental logical flaws. The electron is a negatively charged real particle with a definite physical size and high-frequency transverse oscillation; a single real particle has no physical basis for self-interference. Abandoning the abstract probability wave hypothesis, this paper establishes a complete real-interaction model including electrostatic repulsion deflection, surface electron exchange, collision scattering, microscopic refraction, and barrier diffraction, based on the three-dimensional random transverse oscillation and charge repulsion of electrons. The model uniformly explains the real formation mechanism of electron single-slit diffraction and double-slit interference fringes. This paper proves that in single-electron sequential emission, each electron passes through only one slit; all bright and dark fringes are the statistical result of multiple microscopic interactions between electrons and slit walls or the central barrier. The disappearance of fringes under observation is caused by external disturbance to the inherent oscillation and wall-interaction equilibrium, not by wave function collapse. This paper further clarifies that whether an electron can pass through a slit is determined by its transverse oscillation amplitude, not by wavelength. Amplitude directly corresponds to slit width and is the core controlling variable of diffraction. Meanwhile, if no slit is placed, electrons flying directly to the screen produce no diffraction or interference fringes, proving that electrons themselves have no self-interference ability. Fringes are generated by slit structures, not by intrinsic wave interference of electrons. This study corrects the century-long misunderstanding of electron diffraction and establishes a new microscopic diffraction mechanism consistent with classical real-particle physics.