Related papers: The infinite potential well with moving walls
Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
Coupled triple well (phi6) one-dimensional potentials occur in both condensed matter physics and field theory. Here we provide a set of exact periodic solutions in terms of elliptic functions (domain wall arrays) and obtain single domain…
Using the Caldirola-Kanai Hamiltonian, we study the time evolution of the wave function of a particle whose classical motion is governed by the Langevin equation. We show, in particular, that if the initial wave function is Gaussian, then…
The method of a determination of a quantum wave impedance for an arbitrary piecewise constant potential was developed. On the base of this method both the well-known iterative formula \cite{Khondker_Khan_Anwar:1988} and alternative ways for…
It is shown that a quantum L\'evy process in a box leads to a problem involving topological constraints in space, and its treatment in the framework of the path integral formalism with the L\'evy measure is suggested. The eigenvalue problem…
Motion of a rigid body immersed in a semi-infinite expanse of gas in a $d$-dimensional region bounded by an infinite plane wall is studied for free molecular flow on the basis of the free Vlasov equation under the specular boundary…
Coupled asymmetric double well ($a\phi^2-b\phi^3+c\phi^4$) one-dimensional potentials arise in the context of first order phase transitions both in condensed matter physics and field theory. Here we provide an exhaustive set of exact…
We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…
In this paper we derive an expression for the static electric polarizability of a particle bound by a finite potential well without the explicit use of the continuum states in our calculations. This will be accomplished by employing the…
An infinite well potential containing a rectangular barrier in its center is used to verify if the passage of a quantum particle through the barrier is described by tunnel effect or 'saute-mouton'.
In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem,…
We consider two- and three-dimensional gravity and gravity-capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves…
We are concerned with the reconstruction of a one dimensional wave equation, where the potential is known in a neighborhood of one of the end points of the boundary. We show then the sought potential can be determined by one single…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
In models of phase coexistence, the precise form of the double-well potential is of central importance, yet it cannot be derived from first principles. In this paper, we investigate an inverse problem: starting from a prescribed transition…
We consider some of the methods that can be used to reveal the general features of how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical…
The Euclidean path integral method is applied to a quantum tunneling model which accounts for finite size ($L$) effects. The general solution of the Euler Lagrange equation for the double well potential is found in terms of Jacobi elliptic…
The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the…
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.