Related papers: Zero Energy Solutions and Vortices in Schroedinger…
Neutral atoms interact through a van der Waals potential which asymptotically falls off as r^{-6}. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise…
In this paper we extend the theory of energy solutions for singular SPDEs, focusing on equations driven by highly irregular noise with bilinear nonlinearities, including scaling critical examples. By introducing Gelfand triples and…
In this work we discuss in detail the known solutions of the stationary Schr\"odinger equation subject to a deformable hyperbolic tangent potential exactly soluble $ V(x) = \frac {V_0} {2} (1+ \tanh (\delta x)) $. We find the analytical…
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative…
We study the Ginzburg-Landau equations in order to describe a two-dimensional superconductor in a bounded domain. Using the properties of a particular integrability point ($\kappa = 1/ \sqrt2$) of these nonlinear equations which allows…
Exact analytic solutions to the Schr\"odinger equation for an electron moving in three dimensional potentials have been studied. These solutions can correspond to metals, semiconductors, or insulators. We show that there is an efficient…
Schrodinger's equation predicts something very peculiar about the electron in the Hydrogen atom: its total energy must be equal to zero. Unfortunately, an analysis of a zero-energy wavefunction for the electron in the Hydrogen atom has not…
We study the properties of the Ginzburg-Laundau model in the self-dual point for a two-dimensional finite system . By a numerical calculation we analyze the solutions of the Euler-Lagrange equations for a cylindrically symmetric ansatz. We…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
For any central potential V in D dimensions, the angular Schroedinger equation remains the same and defines the so called hyperspherical harmonics. For non-central models, the situation is more complicated. We contemplate two examples in…
Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to approach the issue of…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
There are various types of infinite potential well problems occurring in elementary quantum mechanics formalism. The infinite square well (one dimensional), cubical box and, spherical well are quite common in textbooks. In this paper, we…
We present a systematic method for constructing static, spherically symmetric regular spacetimes in general relativity satisfying the weak energy condition. Our approach relies on physically reasonable assumptions on the matter energy…
Advantage is taken of the arbitrariness in energy reference to consider anew integral transcriptions of Schrodinger's equation in the presence of potentials which at infinity acquire constant, nonvanishing values. It is found possible to…
We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in the magneto-static case, i.e when the electric potential…
We study the large-time behavior of global energy class ($H^1$) solutions of the one-dimensional nonlinear Schr\"odinger equation with a general localized potential term and a defocusing nonlinear term. By using a new type of interaction…
We consider self-trapping of topological modes governed by the one- and two-dimensional (1D and 2D) nonlinear-Schrodinger/Gross-Pitaevskii equation with effective single- and double-well (DW) nonlinear potentials induced by spatial…
We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from 1 only on finitely many disjoint domains, called the {\it pinning domains}. These…
We present a nonrelativistic wave equation for the electron in (3+1)-dimensions which includes negative-energy eigenstates. We solve this equation for three well-known instances, reobtaining the corresponding Pauli equation (but including…