40 citations · 117 across the 17 of their papers we have counts for
17 papers
Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations
T. A. Ishkhanyan, V. P. Krainov, A. M. Ishkhanyan
We show that there exist infinitely many nontrivial choices of parameters of the single confluent Heun equation for which the three-term recurrence relations governing the expansio…
Rational solutions of (1+1)-dimensional Burgers equation and their asymptotic
V. I. Avrutskiy, V. P. Krainov
A special initial condition for (1+1)-dimensional Burgers equation is considered. It allows to obtain new analytical solutions for an arbitrary low viscosity as well as for the inv…
WKB-approach for the 1D hydrogen atom
A. M. Ishkhanyan, V. P. Krainov
Taking into account results of WKB-approximation, we derive exact quantum energies and wave functions of even and odd states in the one-dimensional Coulomb potential
Uncertainty relation for the radial momentum and radial coordinate in the Coulomb potential
A. M. Ishkhanyan, V. P. Krainov
We have obtained the uncertainty relations for arbitrary states of the hydrogen atom. It is shown that the minimal value of the uncertainty relation is attained for the circular Ry…
Low-frequency electromagnetic radiation of hydrogen molecular gas: effect of the ortho-para conversion
A. M. Ishkhanyan, V. P. Krainov
We calculate the rate of the spontaneous magnetic dipole radiation transitions from ortho- to para-states of the hydrogen molecule at the room temperature with the radiation wavele…
Dissociation of quarkonium in a strong electric field
A. M. Ishkhanyan, V. P. Krainov
The probability of tunnel decay of quarkonium (bond state of a heavy quark and a heavy antiquark) into free quarks in a strong electric field is estimated.
A conditionally integrable bi-confluent Heun potential involving inverse square root and centrifugal barrier terms
T. A. Ishkhanyan, V. P. Krainov, A. M. Ishkhanyan
We present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric fun…
Semiclassical rates for tunnel ionization from power-law potentials induced by a constant or low-frequency electric field
A. M. Ishkhanyan, V. P. Krainov
The probabilities of tunnel ionization of particles confined by one-dimensional power-law and logarithmic potentials are calculated for constant and low-frequency electric fields.
Maslov index for power-law potentials
A. M. Ishkhanyan, V. P. Krainov
The Maslov index in the semiclassical Bohr-Sommerfeld quantization rule is calculated for one-dimensional power-law potentials. The result for the inverse square root potential is…
Discretization of Natanzon potentials
A. Ishkhanyan, V. Krainov
We show that the Natanzon family of potentials is necessarily dropped into a restricted set of distinct potentials involving a fewer number of independent parameters if the potenti…
Non-exponential Auger decay
A. M. Ishkhanyan, V. P. Krainov
We discuss the possibility of non-exponential Auger decay of atoms irradiated by X-ray photons. This effect can occur at times, which are greater than the lifetime of a system unde…
One-dimensional Hubbard-Luttinger model for carbon nanotubes
H. A. Ishkhanyan, V. P. Krainov
A Hubbard-Luttinger model is developed for qualitative description of one-dimensional motion of interacting Pi-conductivity-electrons in carbon single-wall nanotubes at low tempera…
Non-exponential tunneling ionization of atoms by an intense laser field
A. M. Ishkhanyan, V. P. Krainov
We discuss the possibility of non-exponential tunneling ionization of atoms irradiated by intense laser field. This effect can occur at times, which are greater than the lifetime o…
Higher order transmission resonances in above-barrier reflection of ultra-cold atoms
H. A. Ishkhanyan, V. P. Krainov, A. M. Ishkhanyan
The reflectionless transmission resonances in above-barrier reflection of Bose-Einstein condensates by the Rosen-Morse potential are considered using the mean field Gross-Pitaevski…
Transmission resonances in above-barrier reflection of ultra-cold atoms by the Rosen-Morse potential
H. A. Ishkhanyan, V. P. Krainov, A. M. Ishkhanyan
Quantum above-barrier reflection of ultra-cold atoms by the Rosen-Morse potential is analytically considered within the mean field Gross-Pitaevskii approximation. Reformulating the…
Multiple-scale analysis for resonance reflection by a one-dimensional rectangular barrier in the Gross-Pitaevskii problem
H. A. Ishkhanyan, V. P. Krainov
We consider a quantum above-barrier reflection of a Bose-Einstein condensate by a one-dimensional rectangular potential barrier, or by a potential well, for nonlinear Schroedinger…
Above-Barrier Reflection of Cold Atoms by Resonant Laser Light within the Gross-Pitaevskii Approximation
H. A. Ishkhanyan, V. P. Krainov
Above-barrier reflection of cold alkali atoms by resonant laser light was considered analytically within the Gross-Pitaevskii approximation. Correction for the reflection coefficie…