Related papers: Convergence and completeness for square-well Stark…
The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in…
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…
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.
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 study the structure of resonances as derived from the exactly solvable Lippmann-Schwinger equation for a one-dimensional square well potential. Within this framework, we discuss the concept of resonance form factors, and the relation of…
We extend the standard treatment of the asymmetric infinite square well to include solutions that have zero curvature over part of the well. This type of solution, both within the specific context of the asymmetric infinite square well and…
This paper is a direct illustration of a construction of coherent states which has been recently proposed by two of us (JPG and JK). We have chosen the example of a particle trapped in an infinite square-well and also in P\"oschl-Teller…
The particle in a well in dimension one is a classical problem in quantum mechanics. We study higher-dimensional analogues of the problem, where the well is a smooth domain in $\mathbb{R}^d$. We show that simple eigenvalues and…
Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…
The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take…
We study the spectral properties of a Schr\"odinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates,…
The classical square well potential is smoothed with a finite range smoothing function in order to get a new simple strictly finite range form for the phenomenological nuclear potential. The smoothed square well form becomes exactly zero…
We consider a semilinear wave equation in the whole space with a deep potential well. We prove that as the depth of the well tends to infinity, the solutions of the equation converge to the solutions of a wave equation defined on the bottom…
The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical,…
We consider resonant tunneling between disorder localized states in a potential energy displaying perfect correlations over large distances. The phenomenon described here may be of relevance to models exhibiting many-body localization.…
This article is concerned with a special class of the ``double-well-like'' potentials that occur naturally in the analysis of finite quantum systems. Special attention is paid, in particular, to the so-called Fokker-Planck potential, which…
We examine the revival features in wave packet dynamics of a particle confined in a finite square well potential. The possibility of tunneling modifies the revival pattern as compared to an infinite square well potential. We study the…
We prove the equivalence (under some conditions) of two sets of coherent states built for the one-dimensional infinite square well: the so-called generalized and Gaussian Klauder coherent states. We then derive an approximate close…
One of the most widely problem studied in quantum mechanics is of an infinite square-well potential. In a minimal-length scenario its study requires additional care because the boundary conditions at the walls of the well are not well…
A new family of 2-component vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented. They allow a consistent quantization of the classical phase space and observables for a particle in…