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Acta Sinica Quantum Optica

The Velocities of Energy and Traversing Times of Particles Passing Through A Potential Well and Photons TravellingThrough A Thin Glass Plate

Yuwu Zhang

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

A physically meaningful speed-the velocity of energy is used, which is similar to the energy speed in electromagnetism, to describe the process of particles passing through a potential well. It is shown that the corresponding traversing time of particles isn't negative as the phase time, which is negative under certain conditions. This speed can also describe the process of photons travelling through a non-dispersing thin glass plate. The corresponding traversing time of photons isn't negative as the phase time either. We provide an experimental method to test and verify the proposed traversing time. [WT5HZ]

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A physically meaningful speed-the velocity of energy is used, which is similar to the energy speed in electromagnetism, to describe the process of particles passing through a potential well. It is shown that the corresponding traversing time of particles isn't negative as the phase time, which is negative under certain conditions. This speed can also describe the process of photons travelling through a non-dispersing thin glass plate. The corresponding traversing time of photons isn't negative as the phase time either. We provide an experimental method to test and verify the proposed traversing time. [WT5HZ]
To understand the physical meaning of phase time further more, we discuss the reflection phase time of quantum-particles passing though a potential well It is shown that the reflection phase time is equal to the transmission phase time in value and negative under certain conditions for a square potential well by analyzing While quantum-particles passing through the potential well, we think that this course can be described only with the velocity of energy of quantum mechanics whether or not they are reflected or transmitted eventually
The precise definition and physical interpretation of a tunneling time is a fundamental problem in quantum mechanics. The lack of a well-defined time operator in quantum theory precludes the calculation of time in terms of an expectation value. Consequently, model calculations and simulation studies have been proposed and used to determine the time for a particle to traverse a quantum-mechanical barrier. The results offer both qualitatively and quantitatively, disparate predictions. One of the more commonly used approaches is the phase method, which we have applied to several one-dimensional model potentials to show that the tunneling time is characterized by the ratio of the typical decay length in the barrier to the incident velocity, τ∼(1/κ)/v0. We also show that the phase and the spin precession methods are equivalent when the magnetic field is applied throughout the space containing the particle wave function and the tunneling barrier. In principle, the spin precession method can be regarded as an operational definition of the tunneling time. It also has been shown that a tunneling time can be defined operationally for a time-dependent barrier, for which the model calculations predict a tunneling time given by the mean barrier width divided by the magnitude of the imaginary velocity of the particle in the barrier, τ∼d/‖v‖. This pseudokinematic result has been inferred by magnetic field dependent tunneling through heterostructures and computer simulation of wave packet tunneling through one-dimensional square barriers. Other tunneling time theories predict one or the other of the above mentioned characteristic times; several theories predict both. We interpret these different results for τ to mean that a tunneling time is not uniquely defined as a function of particle energy and the barrier shape unless the process in which the tunneling is involved is also specified. That is, the tunneling time is a meaningful and unique concept only for particular tunneling processes or definite operational procedures.
Newton mechanics is great, Newton's contribution is indelible. But from Newton's classical mechanics, the definition of velocity (=) must mean that this physical parameter is a vector, so "negative velocity" only means the opposite direction of motion, no other meaning. It is difficult to understand negative velocity within the framework of classical mechanics. However, wave is a special form of material motion, wave mechanics has a unique method and meaning, and its concept and connotation are significantly different from classical mechanics. For example, wave velocity (whether phase velocity or group velocity) is a scalar quantity. "Negative wave velocity" does not mean that the direction of motion is reversed, but a special phenomenon that does not accord with causality from the surface view. In any case, research in recent decades has shown that negative wave velocity is not only theoretically possible, it has also been repeatedly shown to exist experimentally. Moreover, negative wave velocity is a special form of superluminal speed; The wave with negative velocity is the advanced wave. It corresponds to the leading solution of the basic equation of electromagnetic field and electromagnetic wave. The past practice (discarding the advanced solution) is wrong! As for causality, scientists have provided a new definition and interpretation. In short, both wave mechanics and quantum optics take a different approach from classical mechanics. This paper points out that it is unusual for the 2022 Nobel Prize in Physics to be awarded to Alain Aspect and two others, since Aspect's experiments on the Bell inequality were completed in 1982, Which still stands today as a crucial experiment that proved Einstein's EPR paper wrong and quantum mechanics (QM) correct. Aspect's award in 2022 showed that mainstream physical community had been forced to accept that quantum entanglement existed and that the "light-speed limit" theory of SR was a mistake. This paper discusses the proposition "negative characteristic motion of electromagnetic wave" put forward by the author in 2013, pointing out that it is an inherent physical phenomenon reflecting symmetry in nature. In this paper, the faster-than-light motion of waves found in the near-field of antennas is discussed. In addition, the realizability of "time travel" is also discussed.
We consider the quantum traversal time of an incident wave packet across a potential well using the theory of quantum time of arrival (TOA) operators. This is done by constructing the corresponding TOA operator across a potential well via quantization. The expectation value of the potential-well TOA operator is compared to the free-particle case for the same incident wave packet. The comparison yields a closed-form expression of the quantum well traversal time which explicitly shows the classical contributions of the positive and negative momentum components of the incident wave packet and a purely quantum-mechanical contribution significantly dependent on the well depth. An incident Gaussian wave packet is then used as an example. It is shown that for shallow potential wells, the quantum well traversal time approaches the classical traversal time across the well region when the incident wave packet is spatially broad and approaches the expected quantum free-particle traversal time when the wave packet is localized. For deep potential wells, the quantum traversal time oscillates from positive to negative, implying that the wave packet can be advanced or delayed.