Related papers: The infinite potential well with moving walls

A time evolving fluid system is constructed on a timelike boundary hypersurface at finite cutoff in Vaidya spacetime. The approach used to construct the fluid equations is a direct extension of the ordinary Gravity/Fluid correspondence…

The paper considers a process of escape of classical particle from a one-dimensional potential well by virtue of an external harmonic forcing. We address a particular model of the infinite-range potential well that allows independent…

We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…

It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well, that highly complex behavior of the time evolution of a wave function is associated with the almost degeneracy of levels in the…

We study the wetting model, which considers a random walk constrained to remain above a hard wall, but with additional pinning potential for each contact with the wall. This model is known to exhibit a wetting phase transition, from a…

A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the…

A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a $\delta$-function potential, which appear naturally in the model.…

An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the…

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.

We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded region. Under the assumption of compact support of the…

The integrable time-dependent central potentials that admit linear and quadratic first integrals other than those constructed from the angular momentum are determined. It is shown explicitly that previous answers to this problem are…

This paper presents a new technique to calculate the evolution of a quantum wavefunction in a chosen spatial basis by minimizing the accumulated action. Introduction of a finite temporal basis reduces the problem to a set of linear…

We apply power series expansion to symmetric multi-well oscillators bounded by two infinite walls. The spectrum and expectation values obtained are compared with available exact and approximate values for the unbounded ones. It is shown…

We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…

This article discusses a p-adic version of the infinite potential well in quantum mechanics (QM). This model describes the confinement of a particle in a p-adic ball. We rigorously solve the Cauchy problem for the Schr\"odinger equation and…

Dynamics of cylindrical and spherical relativistic domain walls is investigated with the help of a new method based on Taylor expansion of the scalar field in a vicinity of the core of the wall. Internal oscillatory modes for the domain…

We consider in detail the quantum-mechanical problem associated with the motion of a one-dimensional particle under the action of the double-well potential. Our main tool will be the euclidean (imaginary time) version of the path-integral…

This review is dedicated to some recent results on Weyl theory, inverse problems, evolution of the Weyl functions and applications to integrable wave equations in a semistrip and quarter-plane. For overdetermined initial-boundary value…

In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a "fractional dimensional" wave equation and analyzing the properties of its fundamental solution, we…