84 citations · 384 across the 17 of their papers we have counts for
17 papers
Hermite function solutions of the Schrödinger equation for the sextic oscillator
A. M. Ishkhanyan, G. Lévai
We examine the conditions under which the solution of the radial stationary Schrödinger equation for the sextic anharmonic oscillator can be expanded in terms of Hermite functions.…
Exact solutions of the sextic oscillator from the bi-confluent Heun equation
G. Lévai, A. M. Ishkhanyan
The sextic oscillator is discussed as a potential obtained from the bi-confluent Heun equation after a suitable variable transformation. Following earlier results, the solutions of…
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.…
Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity
A. M. Ishkhanyan
We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinatio…
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 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…
The third exactly solvable hypergeometric quantum-mechanical potential
A. M. Ishkhanyan
We introduce the third independent exactly solvable hypergeometric potential, after the Eckart and the Pöschl-Teller potentials, which is proportional to an energy-independent para…
Schrödinger potentials solvable in terms of the general Heun functions
A. M. Ishkhanyan
We show that there exist 35 choices for the coordinate transformation each leading to a potential for which the stationary Schrödinger equation is exactly solvable in terms of the…
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…
Exact solution of the Schrödinger equation for the inverse square root potential
A. M. Ishkhanyan
We present the exact solution of the stationary Schrödinger equation equation for the potential . Each of the two fundamental solutions that compose the general s…
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.…
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…
Series solutions of confluent Heun equations in terms of incomplete Gamma-functions
A. M. Ishkhanyan
We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical func…
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…
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…