Two-Particle Systems, Potential-Well Bound-State Problems

Ivan F. Melikhov, I. Yu. Popov

The paper deals with the problem of quantum particle storage in a nanolayered structures. The system of a few electrons interacting via a -potential is considered. The particles are placed into a two-dimensional deformed waveguide. From a mathematical point of view, the bound state of the system means that the corresponding Hamiltonian will have eigenvalues. To treat a multi-particle problem, the Hartree-Fock approach and the finite element method are used. Three different types of the perturbation are considered: deformation of the layer boundary, a small window in a wall between two layers and a bent layer. The systems of 2‐10 particles with various total spins are studied. The dependence of the minimal deformation parameter, which keeps bound state on the number of particles, is given. Comparison of the storage efficiencies in those cases is made.

F. Coester

Alexander S. Chikhachev

Bound states of a particle in the field of two pointlike δ centers are considered in the 3D problem. The exact solution to the Schrödinger equation is obtained for a system of scattered centers.

Alberto Galindo, P. Pascual

Bernhard Baumgartner

Examples of bound states are presented, for a system of three identical particles as well as for a system of particles on a lattice. The particles may be bosons as well as fermions. The interaction between them is given by a pair potential, which does not allow two-particle bound states, has positive scattering length and is not too different from realistic interatomic potentials.

Walter Greiner, J. Reinhardt