arXiv subjects

V. R. Khalilov

Publications and source records attributed to V. R. Khalilov.

23 records · Page 2Linked to original sources

arXiv2004

Effect of magnetic fields on bound localized electron states

An approximate analytic solution for the ground electron state are found to the Schroedinger equation for a combination of a uniform magnetic field and single attractive delta-potential. Effect of the magnetic field on this bound localized electron state is discussed. We show that above effect leads to appearing the probability current density in some region centered in the point of the delta-potential as well as to enlarging (for a number of physical models) the localization region of the electron in the plane perpendicular to the magnetic field. We are expected that these properties can be of importance for real quantum mechanical systems.

quant-ph↗

arXiv2000

Planar Dirac Electron in Coulomb and Magnetic Fields

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong magnetic fields, we present the exact recursion relations that determine the coefficients of the series expansion of wave functions, the possible energies and the magnetic fields. It is found that analytic solutions are possible for a denumerably infinite set of magnetic field strengths. This system thus furnishes an example of the so-called quasi-exactly solvable models. A distinctive feature in the Dirac case is that, depending on the strength of the Coulomb field, not all total angular momentum quantum number allow exact solutions with wavefunctions in reasonable polynomial forms. Solutions in the nonrelativistic limit with both attractive and repulsive Coulomb fields are briefly discussed by means of the method of factorization.

quant-ph↗

arXiv2000

Pair Production of charged vector bosons in supercritical magnetic fields at finite temperatures

The thermodynamic properties of an ideal gas of charged vector bosons (with mass m and charge e) is studied in a strong external homogeneous magnetic field no greater than the critical value B_{cr}=m^2/e. The thermodynamic potential, after appropriate analytic continuation, is then used in the study of the spontaneous production of charged spin-one boson pairs from vacuum in the presence of a supercritical homogeneous magnetic field at finite temperature.

hep-th↗

arXiv1998

Dirac electron in a Coulomb Field in 2+1 Dimensions

Exact solutions of Dirac equation in two spatial dimensions in the Coulomb field are obtained. Equation which determines the so-called critical charge of the Coulomb field is derived and solved for a simple model.

hep-th↗

arXiv1996

Two-dimensional electron gas in uniform magnetic and electric fields

The thermodynamic potential of an ideal nonrelativistic gas of two-dimensional electrons in crossed uniform magnetic and electric fields is constructed. For low temperatures and very weak electric fields, it is shown that the Hall conductance is always quantized at integral multiples of $e^2/h$ over a large range of strong magnetic fields. This could be viewed as a quantum statistical explanation of the integral quantum Hall effect. Magnetic properties of the system at high temperatures are briefly discussed.

cond-mat↗