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20112020
most citedSolutions of the bi-confluent Heun equation in terms of the Hermite functions

59 citations

18 papers

quant-ph2020★ 1 cited

Comment on the paper "Third-harmonic generation investigated by a short-range bottomless exponential potential well" by M. Hu, K. Guo, Q. Yu, Z. Zhang [Superlattices and Microstructures, 122 (2018) 538-547]

A. M. Ishkhanyan, G. G. Demirkhanyan

We have discovered several severe errors in the recent paper M. Hu, K. Guo, Q. Yu, Z. Zhang [Superlattices and Microstructures, 122 (2018) 538-547]. Specifically, we demonstrate th…

quant-ph2019★ 1 cited

Bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle

H. H. Azizbekyan, A. M. Manukyan, V. M. Mekhitarian +1

The variety of bi-confluent Heun potentials for a stationary relativistic wave equation for a spinless particle is presented. The physical potentials and energy spectrum of this wa…

hep-th2018★ 6 cited

Scalar Casimir densities and forces for parallel plates in cosmic string spacetime

E. R. Bezerra de Mello, A. A. Saharian, S. V. Abajyan

We analyze the Casimir densities and forces associated with a massive scalar quantum field confined between two parallel plates in a D-dimensional cosmic string spacetime. The plat…

math.NT2018★ 2 cited

A New Method in the Problem of Three Cubes

Armen Avagyan, Gurgen Dallakyan

In the current paper we are seeking P1(y),P2(y),P3(y) with the highest possible degree polynomials with integer coefficients, and Q(y) via the lowest possible degree polynomial, su…

hep-th2018★ 4 cited

Scalar Casimir effect in a linearly expanding universe

A. A. Saharian, T. A. Petrosyan, S. V. Abajyan +1

We investigate quantum vacuum effects for a massive scalar field, induced by two planar boundaries in background of a linearly expanding spatially flat Friedmann-Robertson-Walker s…

quant-ph2017★ 6 cited

A periodic level-crossing two-state model of a general Heun class

G. Saget, A. M. Ishkhanyan, C. Leroy +1

We present a specific constant-amplitude periodic level-crossing model of the semi-classical quantum time-dependent two-state problem that belongs to a general Heun class of field…

quant-ph2016★ 59 cited

Solutions of the bi-confluent Heun equation in terms of the Hermite functions

T. A. Ishkhanyan, A. M. Ishkhanyan

We construct an expansion of the solutions of the bi-confluent Heun equation in terms of the Hermite functions. The series is governed by a three-term recurrence relation between s…

quant-ph2016★ 20 cited

A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions

A. M. Ishkhanyan

We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schrödinger equation is written through the fi…

quant-ph2015★ 31 cited

A conditionally exactly solvable generalization of the inverse square root potential

A. M. Ishkhanyan

We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each…

physics.gen-ph2015

Some non linear interactions in polytropic gas cosmology: Phase space analysis

Martiros Khurshudyan

There are various cosmological models with polytropic equation of state associated to dark energy. Polytropic EoS has important applications in astrophysics, therefore a study of i…

quant-ph2015★ 10 cited

Phase-locking at low-level of quanta

G. H. Hovsepyan, A. R. Shahinyan, Lock Yue Chew +1

We discuss phase-locking phenomena at low-level of quanta for parametrically driven nonlinear Kerr resonator (PDNR) in strong quantum regime. Oscillatory mode of PDNR is created in…

quant-ph2015★ 10 cited

Quantum statistics in time-modulated exciton-photon system

G. Yu. Kryuchkyan, A. R. Shahinyan, I. A. Shelykh

We consider a system consisting of a large individual quantum dot with excitonic resonance coupled to a single mode photonic cavity in the nonlinear regime when exciton- exciton in…

gr-qc2015★ 7 cited

Phase space analysis of some interacting Chaplygin gas models

M. Khurshudyan, R. Myrzakulov

The goal of this paper is to discuss phase space analysis of some interacting Chaplygin gas models in General Relativity. Chaplygin gas is one of the fluids actively considered in…

quant-ph2015★ 32 cited

The Lambert-W step-potential - an exactly solvable confluent hypergeometric potential

A. M. Ishkhanyan

We present an asymmetric step-barrier potential for which the one-dimensional stationary Schrödinger equation is exactly solved in terms of the confluent hypergeometric functions.…

quant-ph2015★ 40 cited

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…

hep-th2014★ 55 cited

Vacuum currents induced by a magnetic flux around a cosmic string with finite core

E. R. Bezerra de Mello, V. B. Bezerra, A. A. Saharian +1

We evaluate the Hadamard function and the vacuum expectation value of the current density for a massive complex scalar field in the generalized geometry of a straight cosmic string…

gr-qc2014★ 6 cited

Quintessence Cosmology with an Effective -Term in Lyra Manifold

M. Khurshudyan, A. Pasqua, J. Sadeghi +1

In this paper, we study quintessence cosmology with an effective -term in Lyra manifold. We consider three different models by choosing variable depend on time, the Hubble p…

astro-ph.SR2011★ 6 cited

Revised classification of the SBS carbon star candidates including the discovery of a new emission line dwarf carbon star

C. Rossi, K. S. Gigoyan, M. G. Avtandilyan +1

Faint high latitude carbon stars are rare objects commonly thought to be distant, luminous giants. For this reason they are often used to probe the structure of the Galactic halo;…