59 citations · 207 across the 16 of their papers we have counts for
17 papers
Inverse square root level-crossing quantum two-state model
T. A. Ishkhanyan, A. V. Papoyan, A. M. Ishkhanyan +1
We introduce a new unconditionally solvable level-crossing two-state model given by a constant-amplitude optical field configuration for which the detuning is an inverse-square-roo…
A Schrödinger potential involving and centrifugal-barrier terms conditionally integrable in terms of the confluent hypergeometric functions
V. A. Manukyan, T. A. Ishkhanyan, A. M. Ishkhanyan
The solution of the one-dimensional Schrödinger equation for a potential involving an attractive and a repulsive centrifugal-barrier terms is presente…
Hypergeometric expansions of the general Heun function governed by two-term recurrence relations
T. A. Ishkhanyan, A. M. Ishkhanyan
We show that there exist infinitely many particular choices of parameters for which the three-term recurrence relations governing the expansions of the solutions of the general Heu…
A new exactly integrable hypergeometric potential for the Schrödinger equation
T. A. Ishkhanyan, V. A. Manukyan, A. H. Harutyunyan +1
We introduce a new exactly integrable potential for the Schrödinger equation for which the solution of the problem may be expressed in terms of the Gauss hypergeometric functions.…
A conditionally integrable Schrödinger potential of a bi-confluent Heun class
T. A. Ishkhanyan, A. M. Manukyan, A. M. Ishkhanyan
We present a bi-confluent Heun potential for the Schrödinger equation involving inverse fractional powers and a repulsive centrifugal-barrier term the strength of which is fixed to…
The third five-parametric hypergeometric quantum-mechanical potential
T. A. Ishkhanyan, A. M. Ishkhanyan
We introduce the third five-parametric ordinary hypergeometric energy-independent quantum-mechanical potential, after the Eckart and Pöschl-Teller potentials, which is proportional…
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…
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…
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…
Four five-parametric and five four-parametric independent confluent Heun potentials for the stationary Klein-Gordon equation
A. S. Tarloyan, T. A. Ishkhanyan, A. M. Ishkhanyan
We present in total fifteen potentials for which the stationary Klein-Gordon equation is solvable in terms of the confluent Heun functions. Because of the symmetry of the confluent…
Analytic solutions of the quantum two-state problem in terms of the double-, bi- and tri-confluent Heun functions
T. A. Shahverdyan, T. A. Ishkhanyan, A. E. Grigoryan +1
We derive five classes of quantum time-dependent two-state models solvable in terms of the double confluent Heun functions, five other classes solvable in terms of the biconfluent…
Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions
T. A. Ishkhanyan, Y. Pashayan-Leroy, M. R. Gevorgyan +2
Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the bico…
A series solution of the general Heun equation in terms of incomplete Beta functions
A. M. Manukyan, T. A. Ishkhanyan, M. V. Hakobyan +1
We show that in the particular case when a characteristic exponent of the singularity at infinity is zero the solution of the general Heun equation can be expanded in terms of the…
Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients
T. A. Ishkhanyan, T. A. Shahverdyan, A. M. Ishkhanyan
We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of…
Confluent hypergeometric expansions of the solutions of the double-confluent Heun equation
T. A. Ishkhanyan, V. A. Manukyan, A. H. Harutyunyan +1
Several expansions of the solutions of the double-confluent Heun equation in terms of the Kummer confluent hypergeometric functions are presented. Three different sets of these fun…
Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions
T. A. Ishkhanyan, A. M. Ishkhanyan
We examine the series expansions of the solutions of the confluent Heun equation in terms of three different sets of the Kummer confluent hypergeometric functions. The coefficients…
New relations for the derivative of the confluent Heun function
V. A. Shahnazaryan, T. A. Ishkhanyan, T. A. Shahverdyan +1
The cases when the equation for the derivative of the confluent Heun function has only three singularities (in general, the equation has four such points) are examined. It is shown…