Related papers: Unexpected Delta-Function Term in the Radial Schro…

We develop a theory of regularity for continuum Schr\"odinger operators based on the Martin compactification of the complement of the essential spectrum. This theory is inspired by Stahl--Totik regularity for orthogonal polynomials, but…

We study the unstable harmonic oscillator and the unstable linear potential in the presence of the point potential, which is the superposition of the Dirac $\delta(x)$ and the derivative $\delta'(x)$. Using the \textit{physical} boundary…

Let -Delta+V be the Schrodinger operator acting on L^2(R^d,C) with d odd larger than 2. Here V is a bounded real- or complex-valued function vanishing outside the closed ball of center 0 and radius a. If V belongs to the class of potentials…

The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation…

It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…

Eigenvalue behaviors of Schr\"odinger operator defined on $n$-dimensional lattice with $n+1$ delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for $n\geq 2$, and lower…

We review and compare two different approaches to radiation reaction in classical electrodynamics of point charges: a local calculation of the self-force using the charge equation of motion and a global calculation consisting in integration…

In this paper we consider the three-dimensional Schr\"{o}dinger operator with a $\delta$-interaction of strength $\alpha > 0$ supported on an unbounded surface parametrized by the mapping $\mathbb{R}^2\ni x\mapsto (x,\beta f(x))$, where…

We present analytically the exact energy bound-states solutions of the Schrodinger equation in $D$-dimensions for a pseudoharmonic potential plus ring-shaped potential of the form $V(r,\theta)=D_{e}(\frac{r}{% r_{e}}-\frac{r_{e}}{r})…

The non-relativistic Schr\"odinger equation on a domain $\Omega\subset \mathbb{R}^d$ with boundary is often considered with homogeneous Dirichlet boundary conditions ($\psi(x)=0$ for $x$ on the boundary), homogeneous Neumann boundary…

We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of…

When the Schr\"{o}dinger equation for stationary states is studied for a system described by a central potential in $n$-dimensional Euclidean space, the radial part of stationary states is an even function of a parameter $\lambda$ which is…

We derive and justify a normal form reduction of the nonlinear Schrodinger equation for a general pitchfork bifurcation of the symmetric bound state that occurs in a double-well symmetric potential. We prove persistence of normal form…

Given a Lipschitz domain $\Omega $ in ${\mathbb R} ^N $ and a nonnegative potential $V$ in $\Omega $ such that $V(x)\, d(x,\partial \Omega)^2$ is bounded in $\Omega $ we study the fine regularity of boundary points with respect to the…

In this work, the analytical solutions of the $D$-dimensional Schr\"odinger equation are studied in great detail for the Wood-Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount…

The paper is concerned with the completeness property of root functions of the Dirac operator with summable complexvalued potential and non-regular boundary conditions. We also obtain explicit form for the fundamental solution system of the…

Selfdual variational calculus is further refined and used to address questions of existence of local and global solutions for various parabolic semi-linear equations, Hamiltonian systems of PDEs, as well as certain nonlinear Schrodinger…

A proof is given that if the nonlinear Schrodinger wave function is constrained to have support over only a finite volume in configuration space, then the total energy is bounded from below for either sign of the logarithmic term in the…

In this paper, we investigate the initial value problem for a Caputo space-time fractional Schrodinger equation for the delta potential. To solve this equation, we use the joint Laplace transform on the spatial coordinate and the Fourier…

Approximate analytical bound state solutions of the radial Schr\"odinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\geq1$ and $q=0$. The energy…