arXiv subjects

Vladimir D. Skarzhinsky

Publications and source records attributed to Vladimir D. Skarzhinsky.

3 recordsLinked to original sources

arXiv2000

Singular potentials and absorption problem in Quantum Mechanics

We discuss a possible approach to the absorption problem in Quantum Mechanics based on using of singular attractive potentials in the corresponding Schrödinger equations. Possible criteria for selection of exact solutions of these equations are considered and it is shown that different models of absorption can be realized by a special choice of exact solutions. As an example, the motion of charged particles in the Aharonov-Bohm (AB) and the scalar attractive $ρ^{-2}$ potentials is investigated in detail. Other attractive potentials are briefly considered.

quant-ph↗

arXiv2000

Elastic scattering and bound states in the Aharonov-Bohm potential superimposed by an attractive $ρ^{-2}$ potential

We consider the elastic scattering and bound states of charged quantum particles moving in the Aharonov-Bohm and an attractive $ρ^{-2}$ potential in a partial wave approach. Radial solutions of the stationary Schrödinger equation are specified in such a way that the Hamiltonian of the problem is self-adjoint. It is shown that they are not uniquely fixed but depend on open parameters. The related physical consequences are discussed. The scattering cross section is calculated and the energy spectrum of bound states is obtained.

quant-ph↗

arXiv1995

A pragmatic approach to the problem of the self-adjoint extension of Hamilton operators with the Aharonov-Bohm potential

We consider the problem of self-adjoint extension of Hamilton operators for charged quantum particles in the pure Aharonov-Bohm potential (infinitely thin solenoid). We present a pragmatic approach to the problem based on the orthogonalization of the radial solutions for different quantum numbers. Then we discuss a model of a scalar particle with a magnetic moment which allows to explain why the self-adjoint extension contains arbitrary parameters and give a physical interpretation.

quant-ph↗