59 citations · 282 across the 16 of their papers we have counts for
16 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 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…
Expansions of the solutions of the general Heun equation in terms of the incomplete Beta functions
T. A. Shahverdyan, V. M. Red'kov, A. M. Ishkhanyan
Applying the approach based on the equation for the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the incomplete Beta functi…
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…
Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
C. Leroy, A. M. Ishkhanyan
We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two…
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…
The Appell hypergeometric expansions of the solutions of the general Heun equation
A. M. Ishkhanyan
Starting from the equation obeyed by the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the Appell generalized hypergeometric…
Thirty five classes of solutions of the quantum time-dependent two-state problem in terms of the general Heun functions
A. M. Ishkhanyan, T. A. Shahverdyan, T. A. Ishkhanyan
We derive 35 five-parametric classes of the quantum time-dependent two-state models solvable in terms of the general Heun functions. Each of the classes is defined by a pair of gen…
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…
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…
Time-dependent level crossing models solvable in terms of the confluent Heun functions
A. M. Ishkhanyan, A. E. Grigoryan
We discuss the level-crossing field configurations for which the quantum time-dependent two-state problem is solvable in terms of the confluent Heun functions. We show that these c…
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…
Incomplete beta-function expansions of the solutions to the confluent Heun equation
Artur Ishkhanyan
Several expansions of the solutions to the confluent Heun equation in terms of incomplete Beta functions are constructed. A new type of expansion involving certain combinations of…