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Publications Influence

New solutions of Heun general equation

- A. Ishkhanyan, K. Suominen
- Mathematics, Physics
- 7 February 2003

We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation. Starting from this property, we use the… Expand

45 4- PDF

Schrödinger potentials solvable in terms of the confluent Heun functions

- A. Ishkhanyan
- Mathematics
- 2 August 2016

We show that if the potential is proportional to an energy-independent continuous parameter, then there exist 15 choices for the coordinate transformation that provide energy-independent potentials… Expand

41 4

A conditionally exactly solvable generalization of the inverse square root potential

- A. Ishkhanyan
- Physics
- 10 November 2015

Abstract We present a conditionally exactly solvable singular potential for the one-dimensional Schrodinger equation which involves the exactly solvable inverse square root potential. Each of the two… Expand

19 2- PDF

Fifteen classes of solutions of the quantum two-state problem in terms of the confluent Heun function

- A. Ishkhanyan, A. É. Grigoryan
- Physics
- 6 February 2014

We derive 15 classes of time-dependent two-state models solvable in terms of the confluent Heun functions. These classes extend over all the known families of three- and two-parametric models… Expand

38 1- PDF

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

- T. Ishkhanyan, A. Ishkhanyan
- Mathematics, Physics
- 7 August 2016

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 successive… Expand

32 1- PDF

Efficient adiabatic tracking of driven quantum nonlinear systems

- S. Guérin, M. Gevorgyan, C. Leroy, H. Jauslin, A. Ishkhanyan
- Physics
- 11 December 2013

5 1

Hypergeometric expansions of the solutions of the general Heun equation governed by two-term recurrence relations for expansion coefficients

- T. Ishkhanyan, T. Shahverdyan, A. Ishkhanyan
- Mathematics
- 31 March 2014

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 which differ from… Expand

10 1

Exact solution of the Schr\"odinger equation for the potential $V_0/{\sqrt{x}}$

- A. Ishkhanyan
- Physics
- 28 August 2015

4 1

Schrödinger potentials solvable in terms of the general Heun functions

- A. Ishkhanyan
- Physics
- 13 January 2016

Abstract We show that there exist 35 choices for the coordinate transformation each leading to a potential for which the stationary Schrodinger equation is exactly solvable in terms of the general… Expand

34- PDF

Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity

- A. Ishkhanyan
- Physics
- 28 February 2018

Abstract.We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinations of the… Expand

14- PDF

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