Related papers: Approximating the ground state eigenvalue via the …
We study analytically the existence and uniqueness of the ground state of the nonlinear Schr\"{o}dinger equation (NLSE) with a general power nonlinearity described by the power index $\sigma\ge0$. For the NLSE under a box or a harmonic…
The ground state of Bose--Einstein condensates can be described as the minimizer of the Gross--Pitaevskii energy functional subject to a mass conservation constraint. In this paper, we study the corresponding discrete optimization problem…
We consider the semi-classical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm-Kova\v{r}\'ik-Portmann and Helffer-Sundqvist for the asymptotics of…
We prove necessary and sufficient conditions for the Schr\"odinger operators to have zero-energy bound states at the threshold of the essential spectrum such that they have bounded $k$-th moment. This result is the extension of the results…
The approximate analytical bound state solution of the Schr\"odinger equation for the Manning-Rosen potential is carried out by taking a new approximation scheme to the orbital centrifugal term. The Nikiforov-Uvarov method is used in the…
One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…
The bound state solutions of the $D$-dimensional Schr\"{o}dinger equation for new mixed class of potential, $V(r)=\frac{V_1}{r^2}+\frac{V_2e^{-\alpha r}}{r}+V_3coth\alpha r+V_4\,,$ are studied within the framework of the Pekeris…
We study the spectral properties of a Schr\"odinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates,…
The ground states of Bose-Einstein condensates in a rotating frame can be described as constrained minimizers of the Gross-Pitaevskii energy functional with an angular momentum term. In this paper we consider the corresponding discrete…
We present exact results for the periodic Anderson model for finite Hubbard interaction 0 <= U < +infinity on certain restricted domains of the model's phase diagram, in d=1 dimension. Decomposing the Hamiltonian into positive semidefinite…
We determine approximate formula for the ground state energy of anyons in 2D parabolic well which is valid for the arbitrary anyonic factor \nu and number of particles N in the system. We assume that centre of mass motion energy is not…
We consider two-component fermions on the lattice in the unitarity limit. This is an idealized limit of attractive fermions where the range of the interaction is zero and the scattering length is infinite. Using Euclidean time projection,…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
We establish a semi-classical formula for the sum of eigenvalues of a magnetic Schrodinger operator in a three-dimensional domain with compact smooth boundary and Neumann boundary conditions. The eigenvalues we consider have eigenfunctions…
We prove quantum dynamical lower bounds for one-dimensional continuum Schr\"odinger operators that possess critical energies for which there is slow growth of transfer matrix norms and a large class of compactly supported initial states.…
We study analytically the radial Schr\"odinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form $V(r)=-\beta_n r^{-n}$ with $n>2$. In particular, assuming that…
We give an overview and extension of recent results on ergodic random Schr\"odinger operators for models on $\mathbb{Z}^d$. The operators we consider are defined on combinatorial or metric graphs, with random potentials, random boundary…
We consider the computations of the action ground state for a rotating nonlinear Schr\"odinger equation. It reads as a minimization of the action functional under the Nehari constraint. In the focusing case, we identify an equivalent…
We study spectral properties of Schr\"odinger operators with random potentials of alloy type on $L^2(\RR)$ and their restrictions to finite intervals. A Wegner estimate for non-negative single site potentials with small support is proven.…
We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schr\"odinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts…