Interpretation of Electron Tunneling from Uncertainty Principle

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...

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...

This article is a slightly expanded version of the talk I delivered at the Special Plenary Session of the 46-th Annual Meeting of the Israel Physical Society (Technion, Haifa, May 11, 2000) dedicated to Misha Marinov. In the first part I briefly discuss quantum tunneling, a topic which Misha cherished and to which he was repeatedly returning through his career. My task was to show that Misha's work had been deeply woven in the fabric of today's theory. The second part is an a...

Tunneling time in attosecond and strong field experiments is one of the most controversial issues in today's research, because of its importance to the theory of time, the time operator and the time-energy uncertainty relation in quantum mechanics. In [1] we derived an estimation of the (real) tunneling time, which shows an excellent agreement with the time measured in attosecond experiments, our derivation is found by utilizing the time-energy uncertainty relation, and it re...

The forerunners preceding the main tunneling signal of the wave created by a source with a sharp onset or by a quantum shutter, have been generally associated with over-the-barrier (non-tunneling) components. We demonstrate that, while this association is true for distances which are larger than the penetration lenght, for smaller distances the forerunner is dominated by under-the-barrier components. We find that its characteristic arrival time is inversely proportional to th...

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 calculate a tunneling time distribution by means of Nelson's quantum mechanics and investigate its statistical properties. The relationship between the average and deviation of tunneling time suggests the exsistence of ``wave-particle duality'' in the tunneling phenomena.

Tunneling is an important physical process. The observation that particles surmount a high mountain in spite of the fact that they don't have the necessary energy cannot be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies pointed towards a universal tunneling time (Haibel,Esposito). Experiments and calcu...

Tunneling is one of the most bizarre phenomena in quantum mechanics. An attempt to understand it led to the next natural question of how long does a particle need to tunnel a barrier. The latter gave rise to several definitions such as the phase, dwell, Larmor and traversal times among others. A short review of the evolution of these time concepts, followed by an account of experiments involving field-induced tunnel ionization and electron tunneling in a solid state junction ...