Related papers: Shape Invariant Single and Double well Potentials …
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the…
We analyze the supersymmetry and the shape invariance of the potentials of the (1+1) relativistic oscillators we have recently proposed.
We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic image $\phi(\partial\Omega)$ of a reference set…
We review basic ideas and basic examples of the theory of the inverse spectral problems.
A behavior of quantum states (superposition of two lowest eigenstates, Gaussian wave packet) in phase space is studied for one and two dimensional double well potential. Two dimensional potential is constructed from double well potential…
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…
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 simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpotentials of dimension $3\times3$ are given…
We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable potentials. Direct problems in terms of spectral functions…
We propose an experiential formula for the calculation of the energy eigenvalues of a particle moving in a one-dimension finite-deep square well potential after some physical considerations. This formula shows a simple relation between the…
We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
The present article deals with differential equations with spectral parameter from the point of view of formal power series. The treatment does not make use of the notion of eigenvalue, but introduces a new idea: the spectral residue. The…
We report on the first direct observation of coherent control of single particle tunneling in a strongly driven double well potential. In our setup atoms propagate in a periodic arrangement of double wells allowing the full control of the…
For an asymmetric double-well potential system, it is shown that, if the potential is quadratic until it reaches several times of the zero-point energies from the bottoms in each well, the energy eigenvalues of the low lying excited states…
The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the…
We introduce a renormalization procedure necessary for the complete description of the energy spectra of a one-dimensional stationary Schr\"odinger equation with a potential that exhibits inverse-square singularities. We apply and extend…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…