Related papers: Particle in infinite potential well with variable …
In its standard formulation, quantum backflow is a classically impossible phenomenon in which a free quantum particle in a positive-momentum state exhibits a negative probability current. Recently, Miller et al. [Quantum 5, 379 (2021)] have…
Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar…
Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities…
In this short paper, we propose a new quantum effect that naturally emerges from describing the quantum particle as a classical fluid. Following the hydrodynamical formulation of quantum mechanics for a particle in a finite convex region,…
Quantum tunneling is a fundamental quantum mechanical effect involved in plenty of physical phenomena. Its control would impact these phenomena and the technologies based on them. We show that the quantum tunneling probability through a…
The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these…
We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the…
We consider a one-dimensional array of particles interacting via an infinite well potential. We explore the properties of energy spreading from an initial state where only a group of particles has non-zero velocities while others are…
In 1989, Deutsch gave a basic physical explanation of why quantum-mechanical probabilities are squares of amplitudes. Essentially, a general state vector is transformed into a highly symmetric equal-amplitude superposition. The argument was…
Quantum backflow is an interference effect in which a matter-wave packet comprised of only plane waves with non-negative momenta exhibits negative probability flux. Here we show that this effect is mathematically equivalent to the…
Since its discovery, quantum theory has proven to be one of the most precise theories ever made. Measurement processes, however, do not seem to be governed by the unitary law of quantum mechanics, and one can ask if the theory is complete.…
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all…
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This…
We show in spatially one dimensional Madelung fluid that a simple requirement on local stability of the maximum of quantum probability density will, if combined with the global scale invariance of quantum potential, lead to a class of…
We consider a single impurity atom trapped in a double well (DW) potential created by a dipolar two-soliton molecule in a quasi-one-dimensional geometry. By solving the eigenvalue problem for the impurity atom in the DW potential, we find…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…
Quantum backflow is a counterintuitive phenomenon in which the probability density of a quantum particle propagates opposite to its momentum. Experimental observation of backflow has remained elusive due to two main challenges: (i) the…
Quantum systems exhibit particle-like or wave-like behaviour depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics, and is fully captured in Wheeler's famous delayed…
Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of…
The resulting stationary states and scattering properties of an effective potential brought about by embedding a quantum well in another well are investigated in this work. The composite well system is constructed via a superposition of…