Potential Barrier Classification by Short-Time Measurement

We investigate the short-time dynamics of a delta-function potential barrier on an initially confined wave-packet. There are mainly two conclusions: A) At short times the probability density of the first particles that passed through the barrier is unaffected by it. B) When the barrier is absorptive (i.e., its potential is imaginary) it affects the transmitted wave function at shorter times than a real potential barrier. Therefore, it is possible to distinguish between an imaginary and a real potential barrier by measuring its effect at short times only on the transmitting wavefunction.Comment: 6 pages, 5 figure

Generic Short-Time Propagation of Sharp-Boundaries Wave Packets

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wavefunction is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times ($t\ll2mx^2/\hbar$, where $x$ is the distance to the boundaries) the wavefunction propagation depends only on the wavefunction's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wavefunction (i.e., for wavepackets with finite-width boundaries) and suggest an experimental verification.Comment: 8 pages, 5 figure

The Paradox of the Recoil Force Acting on a Leaking Water Tank

In the first part of the article, we will outline the paradoxical picture that arises when attempting to calculate the recoil force of the water leakage from a hole at the bottom of a water tank. We will present three different options for the recoil force acting on the water tank as a result of this leakage (in Chapters 1, 2 and 3). In the second part of the article, we will present an experiment that resolves this question (in Chapter 4). Finally (in Chapter 5), we will present a coherent picture of the description of the leakage and the result recoil force.Comment: 19 pages, 6 figurers, 5 graph