Related papers: Particle in infinite potential well with variable …
Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
Quantum backflow is a counterintuitive effect in which the probability density of a free particle moves in the direction opposite to the particle's momentum. If the particle is electrically charged, then the effect can be viewed as the…
We present a class of 2D systems which shows a counterintuitive property that contradicts a semi classical intuition: A 2D quantum particle "prefers" tunneling through a barrier rather than traveling above it. Viewing the one particle 2D…
Among the many perplexing results of quantum mechanics is one that contradicts a result from introductory physics: the possibility of finding a quantum particle in a region that would be forbidden classically by energy conservation. An…
In this work the evolution of a wavefunction in an infinite potential well with time dependent boundaries is investigated. Previous methods for wells with walls moving at a constant velocity are summarised. These methods are extended to…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We first prove that contrary to earlier claims, there is no strong nonlocality: a quantum state localized at the…
The motion of a particle in the potential well is studied when the particle is attached to the infinite elastic string. This is generic with the problem of dissipative quantum mechanics investigated by Caldeira and Leggett. Besides the…
This paper revisits the textbook 'particle in a box', but from the point of view of Koopman-von Neumann (KvN) mechanics. KvN mechanics is a way to describe \emph{classical} dynamics in a Hilbert space. That simple fact changes the usual…
Using the formalism of extended N=4 supersymmetric quantum mechanics we consider the procedure of the construction of multi-well potentials. We demonstrate the form-invariance of Hamiltonians entering the supermultiplet, using the presented…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…
Quantum tunneling is the quantum-mechanical effect where a particle tunnels through a classically forbidden region. Double Square Well Potential (DSWP) is a system where this phenomenon is feasible. Numerous phenomena can be illustrated by…
We examine the classical problem of an infinite square well by considering Hamilton's equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
We study the quantum tunnelling of a very complex object of which only part is coupled to an external potential ( the potential barrier ). We treat this problem as the tunnelling of a particle (part of the system affected by the potential)…
The spectrum of a double well constructed of a square barrier embedded in an infinite well is analyzed. Level statistics for levels slightly above the barrier show signs of Wigner statistics usually associated with quantum chaos. The…
The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain…
Physics has long lived with a schizophrenia that desires determinism for measured systems while demanding that experimenters decide what to measure on a whim. Intriguingly, such a free will assumption for experimenters has thwarted many…
We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.