Related papers: Potential Scattering on a Spherical Surface
We solve the problem of a dimer moving on a spherical surface and find that its binding energy and wave function are sensitive to the total angular momentum. The dimer gets squeezed in the direction orthogonal to the center-of-mass motion…
We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…
A spinless nonrelativistic quantum particle on the curved surface of a homogeneous spherocylindrical capsule is considered. We apply Costa's formalism to solve the Schr\"{o}dinger equation with only a confined potential forcing the particle…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
The potential scattering of electrons carrying non--zero quanta of the orbital angular momentum (OAM) is studied in a framework of the generalized Born approximation, developed in our recent paper by Karlovets \textit{et al.}, Phys. Rev. A.…
The article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic spheres will look if we abandon the standard in the molecular physics assumption that, outside the molecular sphere, in the external…
Scattering phase shift, as a key parameter in scattering theory, plays an important role in characterizing low-energy collisions between ultracold atoms. In this work, we theoretically investigate the universal low-energy behavior of the…
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…
The study of particle motion on spherical surfaces is relevant to adsorption on buckyballs and other solid particles. This paper reports results for the binding energy of such dimers, consisting of two light particles (He atoms or hydrogen…
We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any…
Scattering states with LEED asymptotics are calculated for a general non-muffin tin potential, as e.g. for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction…
As a submanifold is embedded into higher dimensional flat space, quantum mechanics gives various embedding quantities, e.g., the geometric momentum and geometric potential, etc. For a particle moving on a two-dimensional sphere or a free…
The exact two-particle energy eigenstates in an asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum are…
In the da Costa's thin-layer approach, a quantum particle moving in a 3D sample is confined on a curved thin interface. At the end, the interface effects are ignored and such quantum particle is localized on a curved surface. A geometric…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
We study the threshold scattering problem for the energy-critical nonlinear Schr\"odinger equation with a repulsive inverse-square potential $\frac{a}{|x|^2} > 0$ in dimensions $d= 4, 5, 6$. On the energy level surface determined by the…
We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any nonrelativistic effective theory of point particles on the lattice. In the…
Six-dimensional quantum dynamical calculations of the scattering of H_2 from a Pd(100) surface using a potential energy surface derived from density-functional theory calculations are presented. Due to the corrugation and anisotropy of the…
We investigate the on-shell approximation in the context of s-wave scattering for ultracold two-body collisions. Our analysis systematically covers spatial dimensions D=1,2,3 , with the aim of identifying the regimes in which the…