ﻻ يوجد ملخص باللغة العربية
Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is applied, the construction of the necessary resolvents is reviewed and several new ones are introduced. In addition, previous work on the singular harmonic oscillator model, introduced by Avakian et al. is reproduced to verify the method and results. A novel features is the determination of the spectra of asymmetric hybrid linear and quadratic potentials. As in previous work, the singular perturbations are modeled by delta functions.
In this paper we investigate the one-dimensional harmonic oscillator with a singular perturbation concentrated in one point. We describe all possible selfadjoint realizations and we show that for certain conditions on the perturbation exactly one neg
We examine in this article the one-dimensional, non-local, singular SPDE begin{equation*} partial_t u ;=; -, (-Delta)^{1/2} u ,-, sinh(gamma u) ,+, xi;, end{equation*} where $gammain mathbb{R}$, $(-Delta)^{1/2}$ is the fractional Laplacian of order $
We study the singular perturbation of an elastic energy with a singular weight. The minimization of this energy results in a multi-scale pattern formation. We derive an energy scaling law in terms of the perturbation parameter and prove that, althoug
The eigenvalues of the potentials $V_{1}(r)=frac{A_{1}}{r}+frac{A_{2}}{r^{2}}+frac{A_{3}}{r^{3}}+frac{A_{4 }}{r^{4}}$ and $V_{2}(r)=B_{1}r^{2}+frac{B_{2}}{r^{2}}+frac{B_{3}}{r^{4}}+frac{B_{4}}{r^ {6}}$, and of the special cases of these potentials su
We study the one-dimensional Schrodinger operators $$ S(q)u:=-u+q(x)u,quad uin mathrm{Dom}left(S(q)right), $$ with $1$-periodic real-valued singular potentials $q(x)in H_{operatorname{per}}^{-1}(mathbb{R},mathbb{R})$ on the Hilbert space $L_{2}left(m