Related papers: On the accuracy of a recent regularized nuclear po…
The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of…
Given two spherically symmetric and short range potentials $V_0$ and V_1 for which the radial Schrodinger equation can be solved explicitely at zero energy, we show how to construct a new potential $V$ for which the radial equation can…
The Born approximation of a potential in the context of the Calder\'on inverse problem is an object that can be formally defined in terms of spectral data of the Dirichlet-to-Neumann map of the corresponding Schr\"odinger operator. In this…
We show that efficient norm-conserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills…
In this work we study the quantum system with the symmetric Razavy potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun functions. The eigenvalues have to be calculated numerically.…
Nuclear transparency in (e,e'p) reactions is evaluated in a fully relativistic distorted wave impulse approximation model. The relativistic mean field theory is used for the bound state and the Pauli reduction for the scattering state,…
We prove an explicit weighted estimate for the semiclassical Schr\"odinger operator $P = - h^2 \partial^2_x + V(x;h)$ on $L^2(\mathbb{R})$, with $V(x;h)$ a finite signed measure, and where $h >0$ is the semiclassical parameter. The proof is…
A general quantization rule for bound states of the Schrodinger equation is presented. Like fundamental theory of integral, our idea is mainly based on dividing the potential into many pieces, solving the Schr\"odinger equation, and…
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…
Low-lying shell model states may be approximated accurately by a sum over products of proton and neutron states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue…
We investigate the extent to which the nuclear transverse response to electron scattering in the quasielastic region, evaluated in the random-phase approximation can be described by ring approximation calculations. Different effective…
We study one-loop quantum gravity corrections to the standard model Higgs potential $V(\phi)$ $\grave{\rm a}$ la Coleman-Weinberg and examine the stability question of $V(\phi)$ in the energy region of Planck mass scale, $\mu\simeq M_{\rm…
This paper investigates phase retrieval using the Reshaped Wirtinger Flow (RWF) algorithm, focusing on recovering target vector $\vx \in \R^n$ from magnitude measurements \(y_i = \left| \langle \va_i, \vx \rangle \right|, \; i = 1, \ldots,…
We suggest that at any given order of Feynman diagram calculation all renormalization group (RG)-predictable terms should be resummed to all-orders. This ``complete'' RG-improvement (CORGI) serves to separate the perturbation series into…
We study the radial Schr\"{o}dinger equation for a particle of mass $m$ in the field of the inverse-square potential $\alpha/r^{2}$ in the medium-weak-coupling region, i.e., with $-1/4\leq2m\alpha/\hbar^{2}\leq3/4$. By using the…
We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 correction. The power-counting rule, an important ingredient of effective…
We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the $\ell_0$ norm under a tight…
Lemma 4.8 in the article [Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions, Electronic J. Probability 21 (18):1-48 (2016), arXiv:1504.02953] contains a mistake, which implies a weaker regularity…
We present a polymer quantization of the -lambda/r^2 potential on the positive real line and compute numerically the bound state eigenenergies in terms of the dimensionless coupling constant lambda. The singularity at the origin is handled…
We present the exact solution of the stationary Schr\"odinger equation equation for the potential $V=V_0/{\sqrt{x}}$. Each of the two fundamental solutions that compose the general solution of the problem is given by a combination with…