相关论文: Bound States in one and two Spatial Dimensions
We have used different methods to obtain the bound states of a Hamiltonian of a relativistic two scalar particle system in a local potential. The potentials we are interested in are binding and confining potentials, that are associated with…
We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B_2, the binding energies…
The variation of the size of two-body objects is investigated, as the separation energy approaches zero, with both long range potentials and short range potentials having a repulsive core. It is shown that long range potentials can also…
We study the critical behaviour near the threshold where a first bound state appears at some value of coupling constant in an attractive short-range potential in $2+\epsilon $ dimensions. We obtain general expression for the binding energy…
Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schr\"odinger equation is used to…
In the framework of non-relativistic quantum mechanics and with the help of the Greens functions formalism we study the behavior of weakly bound states as they approach the continuum threshold. Through estimating the Green's function for…
A potential of pointlike mass in the partially compactified multidimensional space is considered. The problem is reduced to the multidimensional Poisson equation with the Dirac comb source in r.h.s. Explicit solutions are built in the cases…
The effect of open boundary conditions for four models with quenched disorder are studied in finite samples by numerical ground state calculations. Extrapolation to the infinite volume limit indicates that the configurations in ``windows''…
Simulations of quantum systems in finite volume have proven to be a useful tool for calculating physical observables. Such studies to date have focused primarily on understanding the volume dependence of binding energies, from which it is…
We discuss possibility of upper-bounding dimension of quantum states device-independently. Provided that the states are pure, it is possible to generate certain four states whose dimension is bounded by two.
Macro properties of cold atomic gases are driven by few-body correlations, even if the gas has thousands of particles. Quantum systems composed of two and three particles with attractive zero\=/range pairwise interactions are considered for…
We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for…
Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches'' this procedure does not involve the use of delta-function constraints on the…
Two-particle lattice states are important for physics of magnetism, superconducting oxides, and cold quantum gases. The quantum-mechanical lattice problem is exactly solvable for finite-range interaction potentials. A two-body Schroedinder…
The problem of bound states in a double delta potential is revisited by means of Fourier sine and cosine transforms
One-dimensional scattering by a Coulomb potential V(x)=lambda/|x| is studied for both repulsive (c>0) and attractive (c<0) cases. Two methods of regularizing the singularity at x=0 are used, yielding the same conclusion, namely, that the…
Low-energy two-dimensional scattering is particularly sensitive to the existence and properties of weakly-bound states. We show that interaction potentials $V(r)$ with vanishing zero-momentum Born approximation $\int d^2r V(r)=0$ lead to an…
We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter…
We have discovered an unexpected and surprising fact: a 2D axially symmetric short-range potential contains {\it infinite} number of the levels of negative energy {\it if one takes into account the spin-orbit (SO) interaction.} For a…
In quantum mechanics students are taught to practice that eigenfunction of a physical bound state must be continuous and vanishing asymptotically so that it is normalizable in $x\in (-\infty, \infty)$. Here we caution that such states may…