Quantum Mechanics as a Classical Theory XIII: The Tunnel Effect

Quantum tunneling is considered from the point of view of local realism. It is concluded that a quantum object tunneling through a potential barrier cannot be interpreted as a point-like particle because such an interpretation generates a contradiction with the impossibility of faster-than-light motion. Such a contradiction does not arise if a quantum object is considered as a continuous medium formed by the fields of matter. The dynamics law of the mechanical motion of these...

We present a study of student understanding of energy in quantum mechanical tunneling and barrier penetration. This paper will focus on student responses to two questions that were part of a test given in class to two modern physics classes and in individual interviews with 17 students. The test, which we refer to as the Quantum Mechanics Conceptual Survey (QMCS), is being developed to measure student understanding of basic concepts in quantum mechanics. In this paper we expl...

In this article, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles, by a careful treatment of temporal observables in quantum theory and through a precise application of the duality between particles and waves. To this end, we employ a new method for constructing probabilities associated to quantum time measurements that provides an explicit link between the tunneling time of particles and the associated quantum fields. We demo...

There remains the old question of how long a quantum particle takes to tunnel through a potential barrier higher than its incident kinetic energy. In this article a solution of the question is proposed on the basis of a realistic explanation of quantum mechanics. The explanation implies that the tunneling particle has a certain chance to borrow enough energy from self-interference to high-jump over the barrier. The root-mean-square velocity and the effective tunneling time of...

Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the set of dynamical possibilities arising in simple systems that contain at least some chaotic motion. These tunneling phenomena can be identified by their novel $\hbar$-dependencies and/or statistical behaviors. We summarize a sampling of thes...

In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be described in terms of classical physics without invoking violations of the energy conservation law at any time instance. A formula is presented that generates a wide class of potential barrier shapes with the desirable reflection (transmission) c...

After the review by Hauge and Stovneng the old question of "How long does it take to tunnel through the barrier?" has not still lost its relevance. As before, there is no clear answer to this question even for the one-dimensional completed scattering (OCS). In this paper we show that this seemingly simple question stands alongside with such fundamental problems of quantum mechanics (QM) as the Schrodinger's-cat and and EPR-Bohm paradoxes. Their common feature is that the stat...

Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new experimental techniques revived the issue and ignited a debate with often contradictory results. This motivates the present study of an exactly solvable model for quantum tunneling induced by a strong field. We show that the tunneling dynamics can d...

It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to Aharonov {\it et al.}, and hence describe the outcomes of real measurements made on subensembles. In particular, this approach is used to address the question of the history of a particle which has tunnelled across a barrier. A {\it gedank...

We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. Analyzing solutions with small (complex) energy, relevant for constructing the wave function after a long time, we unravel the analytic structure of the action, and show explicitly how the imaginary time bounce arises as a parameterization of the lowest order term in the energy expansion. The real time cal...