Abstract We provide a semiclassical description of the double-slit experiment given by the momentous quantum mechanics. This formulation allows the study of quantum systems by an effective augmented Hamiltonian. The use of canonical variables enables us to comprise all the quantum information into a finite system of equations. We show the evolution of individual particles and their semiclassical trajectories, and how their collective behavior seems to reproduce the well-known quantum interference pattern. We are able to follow the individual evolution of each particle and its interaction with the effective quantum potential, showing that, contrary to the non-crossing rule present in Bohmian mechanics, particle trajectories actually cross each other in our description. By discussing the quantum-effective potential obtained, we mention possible extensions and applications to other areas.
Abstract We provide a semiclassical description of the double-slit experiment given by the momentous quantum mechanics. This formulation allows the study of quantum systems by an effective augmented Hamiltonian. The use of canonical variables enables us to comprise all the quantum information into a finite system of equations. We show the evolution of individual particles and their semiclassical trajectories, and how their collective behavior seems to reproduce the well-known quantum interference pattern. We are able to follow the individual evolution of each particle and its interaction with the effective quantum potential, showing that, contrary to the non-crossing rule present in Bohmian mechanics, particle trajectories actually cross each other in our description. By discussing the quantum-effective potential obtained, we mention possible extensions and applications to other areas.
In this work, we study the quantum tunnel effect through a potential barrier within a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution of the system is given in terms of a dynamical system for which we are able to determine numerical effective trajectories for individual particles, similar to the Bohmian description of quantum mechanics. We obtain a complete description of the possible trajectories of the system, finding semiclassical reflected, tunneled and confined paths due to the appearance of an effective time-dependent potential.
This article examines the double-slit experiment from a configurational perspective and compares it with the standard quantum-mechanical, Bohmian, and Many-Worlds interpretations. Rather than focusing on microscopic trajectories or wavefunction collapse, the work argues that the central question posed by the experiment is not “how” individual particles behave, but “why” a stable interference pattern emerges with overwhelming statistical certainty. By framing the experiment in terms of constrained configuration spaces and typicality, the article shows that interference can be understood as an inevitable macroscopic outcome, not a mysterious dynamical process.
Abstract Young’s double slit experiments, which represent the mystery of quantum mechanics, have been interpreted by quantum probability waves and de Broglie-Bohm’s trajectory/pilot waves. To study in detail, the double slit experiments are extended to the cross double slit experiments. We argue that an interpretation must be able to explain all of the double slit and cross double slit experiments consistently. To test the interpretations, the comprehensive double slit experiments have been performed, which challenge both the wave interpretation and the trajectory interpretation. The cross double slit experiments and comprehensive double slit experiments provide a new tool for studying the mystery of double slit, wave-particle duality, complementarity principle, wave theory and trajectory theory. In this article, we review the cross double slit experiments and comprehensive double slit experiments, and report new experiments.
One of the intriguing mystery in modern physics is the quantum interference phenomena, which the behaviour of photons in double-slit experiment is still ambiguous.Instead of relying on the naive probabilistic point of view, Bohmian mechanics provides the ground base for interpreting quantum system in a deterministic way closely related to classical mechanics such as it constructs the photon trajectory for the double-slit set up.The appearance on the bending in the constructed photon trajectory seem to contravene the notable law of conservation of momentum.Here, we report on conservation of the transverse momentum of photon trajectories based on numerical solution of Bohmian mechanics in double-slit set up for single photon, pair of photons and ensemble of photons until interference pattern is produced.It is shown that the total transverse momentum in the system of Bohmian mechanics is invariance due to the non-local action of quantum potential.
The causal quantum mechanics (i.e. Bohmian or de Broglie-Bohm or Bohm-de Broglie quantum mechanics) has made possible to calculate the trajectories of electrons in a typical double-slit experiment [C. Philippidis et al., Il Nuovo Cimento, 52 B, 15-28 (1979)]. The trajectories do not correspond to an uniform movement but to an accelerated one. The acceleration is caused by the quantum potential. From the quantum theoretical point of view, there is a probability for the electron to emit photons, with a certain emission power, during its movement from the slits to the screen. We find a quantum general formula for the emission power of photons, valid independently of the interpretation. Then, according to the Copenhagen interpretation, this formula gives a strictly zero value for the emission power because the electron moves as a free particle after it leaves the slit and before reach the screen. Then, there is no emission of photons. In the case of the causal interpretation, the emission power results, for a concrete real experiment, in a very tiny but not a zero value, driven by the square of the quantum potential gradient. We give an idea of the type of spectrum that could be measured. A brief idea of a possible experimental arrangement in order to detect this effect, is given.
Young’s double slit experiments, which represent the mystery of quantum mechanics (Feynman), have been described by optics, electromagnetic wave theory, quantum wave theory and Bohm’s trajectory theory. The double slit has the varieties of the applications. To test the description theories, we perform the comprehensive double slit experiments, which show that (1) before passing through the double slit/cross-double slit and before landing on the screen, the laser light behaves as particles, not as waves; (2) the experiments challenge the computer simulation of the trajectory theory at near field, however support the trajectory theory at far field. Those novel phenomena provide the comprehensive information for further theoretical development and applications.